decompwlj 3D

All 5000 sequences

Every sequence in decompwlj 3D, by A-number, with the share of its decomposable terms in the level class (k > L). Each has its own page with its weight–level plate and counts, and opens in the interactive 3-D viewer.

A-numberNameFamilyLevel
A000027The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguousbase case9.6 %
A000028Let k = p_1^e_1 p_2^e_2 p_3^e_3 ... be the prime factorization of n. Sequence gives k such that the sum of the numbers of 1's in the binary expansions of e_1, e_2, e_3, ... is oddmultiplicative12.7 %
A000037Numbers that are not squares (or, the nonsquares)complement9.6 %
A000040The prime numbersprimes23.0 %
A000062A Beatty sequence: a(n) = floor(n/(e-2))Beatty11.2 %
A000069Odious numbers: numbers with an odd number of 1's in their binary expansionbinary rule11.0 %
A000093a(n) = floor(n^(3/2))polynomial46.6 %
A000096a(n) = n*(n+3)/2polynomial100.0 %
A000124Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cutspolynomial100.0 %
A000125Cake numbers: maximal number of pieces resulting from n planar cuts through a cube (or cake): C(n+1,3) + n + 1polynomial100.0 %
A000201Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622Beatty12.2 %
A000212a(n) = floor(n^2/3)polynomial100.0 %
A000217Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + npolynomial100.0 %
A000290The squares: a(n) = n^2polynomial100.0 %
A000292Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6polynomial100.0 %
A000297a(n) = (n+1)*(n+3)*(n+8)/6polynomial100.0 %
A000326Pentagonal numbers: a(n) = n*(3*n-1)/2polynomial100.0 %
A000330Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2*n+1)/6polynomial100.0 %
A000378Sums of three squares: numbers of the form x^2 + y^2 + z^2quadratic form8.5 %
A000379Numbers where total number of 1-bits in the exponents of their prime factorization is even; a 2-way classification of integers: complement of A000028multiplicative12.7 %
A000384Hexagonal numbers: a(n) = n*(2*n-1)polynomial100.0 %
A000401Numbers of form x^2 + y^2 + 2*z^2quadratic form10.4 %
A000404Numbers that are the sum of 2 nonzero squaresquadratic form16.0 %
A000408Numbers that are the sum of three nonzero squaresquadratic form8.6 %
A000415Numbers that are the sum of 2 but no fewer nonzero squaresmultiplicative16.0 %
A000419Numbers that are the sum of 3 but no fewer nonzero squaresquadratic form12.6 %
A000430Primes and squares of primesmultiplicative23.0 %
A000447a(n) = 1^2 + 3^2 + 5^2 + 7^2 + ... + (2*n-1)^2 = n*(4*n^2 - 1)/3polynomial100.0 %
A000566Heptagonal numbers (or 7-gonal numbers): n*(5*n-3)/2polynomial100.0 %
A000567Octagonal numbers: n*(3*n-2). Also called star numberspolynomial100.0 %
A000578The cubes: a(n) = n^3polynomial100.0 %
A000695Moser-de Bruijn sequence: sums of distinct powers of 4binary rule14.0 %
A000787Strobogrammatic numbers: the same upside downdigit rule93.4 %
A000788Total number of 1's in binary expansions of 0, ..., nsummatory24.1 %
A000959Lucky numberssieve32.3 %
A000960Flavius Josephus's sieve: Start with the natural numbers; at the k-th sieving step, remove every (k+1)-st term of the sequence remaining after the (k-1)-st sieving step; iteratesieve96.6 %
A000961Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1)powers23.0 %
A000966n! never ends in this many 0'sdigit rule19.4 %
A000977Numbers that are divisible by at least three different primesmultiplicative13.8 %
A001043Numbers that are the sum of 2 successive primesprimes24.9 %
A001082Generalized octagonal numbers: k*(3*k-2), k=0, +- 1, +- 2, +-3, ..polynomial100.0 %
A001093a(n) = n^3 + 1polynomial100.0 %
A001097Twin primesprimes19.7 %
A001101Moran numbers: k such that k/(sum of digits of k) is primedigit rule35.6 %
A001105a(n) = 2*n^2polynomial100.0 %
A0011069-gonal (or enneagonal or nonagonal) numbers: a(n) = n*(7*n-5)/2polynomial100.0 %
A00110710-gonal (or decagonal) numbers: a(n) = n*(4*n-3)polynomial100.0 %
A001122Primes with primitive root 2primes30.5 %
A001132Primes == +-1 (mod 8)primes28.3 %
A001196Double-bitters: only even length runs in binary expansionbinary rule14.0 %
A001248Squares of primespowers100.0 %
A001318Generalized pentagonal numbers: m*(3*m - 1)/2, m = 0, +-1, +-2, +-3, ...polynomial77.6 %
A001358Semiprimes (or biprimes): products of two primesmultiplicative15.7 %
A001359Lesser of twin primesprimes47.8 %
A001363Primes in ternarydigit rule27.9 %
A001463Partial sums of A001462; also a(n) is the last occurrence of n in A001462self-referential55.9 %
A001481Numbers that are the sum of 2 squaresmultiplicative15.9 %
A001504a(n) = (3*n+1)*(3*n+2)polynomial100.0 %
A001513a(n) = (6*n+1)*(6*n+5)polynomial100.0 %
A001526a(n) = (7*n+1)*(7*n+6)polynomial100.0 %
A001533a(n) = (8*n+1)*(8*n+7)polynomial100.0 %
A001534a(n) = (9*n+1)*(9*n+8)polynomial100.0 %
A001535a(n) = (10n+1)*(10n+9)polynomial100.0 %
A001536a(n) = (11*n+1)*(11*n+10)polynomial100.0 %
A001538a(n) = (12*n+1)*(12*n+11)polynomial100.0 %
A001539a(n) = (4*n+1)*(4*n+3)polynomial100.0 %
A001545a(n) = (5*n+1)*(5*n+4)polynomial100.0 %
A001597Perfect powers: m^k where m > 0 and k >= 2powers99.3 %
A001633Numbers with an odd number of digitsdigit rule9.2 %
A001637Numbers with an even number of digitsdigit rule8.7 %
A001651Numbers not divisible by 3forced divisor0.0 %
A001690Non-Fibonacci numberscomplement9.6 %
A001694Powerful numbers, definition (1): if a prime p divides n then p^2 must also divide n (also called squareful, square full, square-full or 2-powerful numbers)multiplicative71.9 %
A001704a(n) = n concatenated with n + 1digit rule100.0 %
A001729List of numbers whose digits contain no loops (version 1)digit rule15.0 %
A001740Squares written in base 5digit rule100.0 %
A001741Squares written in base 6digit rule100.0 %
A001742Numbers whose digits contain no loops (version 2)digit rule17.1 %
A001743Numbers in which every digit contains at least one loop (version 1)digit rule13.5 %
A001744Numbers n such that every digit contains a loop (version 2)digit rule13.7 %
A001745Numbers such that at least one digit contains a loop (version 2). Also called "holey" or "holy" numbersdigit rule9.8 %
A001746At least one digit contains a loop (version 1)digit rule9.9 %
A001748a(n) = 3 * prime(n)primes23.0 %
A001749Primes multiplied by 4primes23.0 %
A001751Primes together with primes multiplied by 2primes15.3 %
A001768Sorting numbers: number of comparisons for merge insertion sort of n elementssummatory28.3 %
A001838Numbers k such that phi(k+2) = phi(k) + 2divisor functions44.8 %
A001840Expansion of g.f. x/((1 - x)^2*(1 - x^3))polynomial65.7 %
A001844Centered square numbers: a(n) = 2*n*(n+1)+1. Sums of two consecutive squares. Also, consider all Pythagorean triples (X, Y, Z=Y+1) ordered by increasing Z; then sequence gives Z valuespolynomial100.0 %
A001845Centered octahedral numbers (crystal ball sequence for cubic lattice)polynomial100.0 %
A001855Sorting numbers: maximal number of comparisons for sorting n elements by binary insertionsummatory32.0 %
A001859Triangular numbers plus quarter-squares: n*(n+1)/2 + floor((n+1)^2/4) (i.e., A000217(n) + A002620(n+1))polynomial100.0 %
A001912Numbers k such that 4*k^2 + 1 is primeprime values23.9 %
A001913Full reptend primes: primes with primitive root 10primes30.7 %
A001950Upper Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi^2), where phi = (1+sqrt(5))/2Beatty15.4 %
A001951A Beatty sequence: a(n) = floor(n*sqrt(2))Beatty11.4 %
A001952A Beatty sequence: a(n) = floor(n*(2 + sqrt(2)))Beatty17.2 %
A001953a(n) = floor((n + 1/2) * sqrt(2))Beatty11.3 %
A001954a(n) = floor((n+1/2)*(2+sqrt(2))); winning positions in the 2-Wythoff gameBeatty17.3 %
A001961A Beatty sequence: floor(n * (sqrt(5) - 1))Beatty10.6 %
A001969Evil numbers: nonnegative integers with an even number of 1's in their binary expansionbinary rule11.4 %
A001974Numbers that are the sum of 3 distinct squares, i.e., numbers of the form x^2 + y^2 + z^2 with 0 <= x < y < zquadratic form8.6 %
A001983Numbers that are the sum of 2 distinct squares: of form x^2 + y^2 with 0 <= x < yquadratic form16.0 %
A002035Numbers that contain primes to odd powers onlymultiplicative10.1 %
A002061Central polygonal numbers: a(n) = n^2 - n + 1polynomial100.0 %
A002081Numbers congruent to {2, 4, 8, 16} (mod 20)residue class0.0 %
A002088Sum of totient function: a(n) = Sum_{k=1..n} phi(k), cf. A000010summatory87.3 %
A002113Palindromes in base 10digit rule71.7 %
A002144Pythagorean primes: primes of the form 4*k + 1primes28.0 %
A002145Primes of the form 4*k + 3primes28.2 %
A002202Values taken by totient function phi(m) (A000010)divisor functions12.6 %
A002327Primes of the form k^2 - k - 1primes100.0 %
A002328Numbers k such that k^2 - k - 1 is primeprime values20.3 %
A002378Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1)polynomial100.0 %
A002383Primes of form k^2 + k + 1primes100.0 %
A002384Numbers m such that m^2 + m + 1 is primeprime values24.7 %
A002407Cuban primes: primes which are the difference of two consecutive cubesprimes100.0 %
A002411Pentagonal pyramidal numbers: a(n) = n^2*(n+1)/2polynomial100.0 %
A002412Hexagonal pyramidal numbers, or greengrocer's numberspolynomial100.0 %
A002413Heptagonal (or 7-gonal) pyramidal numbers: a(n) = n*(n+1)*(5*n-2)/6polynomial100.0 %
A002414Octagonal pyramidal numbers: a(n) = n*(n+1)*(2*n-1)/2polynomial100.0 %
A002440Squares written in base 7digit rule100.0 %
A002441Squares written in base 8digit rule100.0 %
A002442Squares written in base 9digit rule100.0 %
A002476Primes of the form 6m + 1primes35.2 %
A002479Numbers of the form x^2 + 2*y^2quadratic form14.9 %
A002480Numbers of the form 2x^2 + 3y^2quadratic form22.3 %
A002481Numbers of form x^2 + 6y^2quadratic form22.8 %
A002492Sum of the first n even squares: a(n) = 2*n*(n+1)*(2*n+1)/3polynomial100.0 %
A002496Primes of the form k^2 + 1primes100.0 %
A002522a(n) = n^2 + 1polynomial100.0 %
A002620Quarter-squares: a(n) = floor(n/2)*ceiling(n/2). Equivalently, a(n) = floor(n^2/4)polynomial100.0 %
A002623Expansion of 1/((1-x)^4*(1+x))polynomial100.0 %
A002717a(n) = floor(n(n+2)(2n+1)/8)polynomial100.0 %
A002731Numbers k such that (k^2 + 1)/2 is primeprime values33.0 %
A002796Numbers that are divisible by each nonzero digitdigit rule13.9 %
A002808The composite numbers: numbers n of the form x*y for x > 1 and y > 1complement10.6 %
A002815a(n) = n + Sum_{k=1..n} pi(k), where pi() = A000720summatory70.2 %
A002821a(n) = nearest integer to n^(3/2)polynomial46.9 %
A002822Numbers m such that 6m-1, 6m+1 are twin primesprimes31.7 %
A002837Numbers k such that k^2 - k + 41 is primeprime values16.1 %
A002858Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier termsself-referential21.9 %
A002859a(1) = 1, a(2) = 3; for n >= 3, a(n) is smallest number that is uniquely of the form a(j) + a(k) with 1 <= j < k < nself-referential20.6 %
A002939a(n) = 2*n*(2*n-1)polynomial100.0 %
A002943a(n) = 2*n*(2*n+1)polynomial100.0 %
A002970Numbers k such that 4*k^2 + 9 is primeprime values23.3 %
A002971Numbers k such that 4*k^2 + 25 is primeprime values18.8 %
A002977Klarner-Rado sequence: a(1) = 1; subsequent terms are defined by the rule that if m is present so are 2m+1 and 3m+1self-referential23.6 %
A002984a(0) = 1; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1)))self-referential100.0 %
A003052Self numbers or Colombian numbers (numbers that are not of the form m + sum of digits of m for any m)digit rule24.9 %
A003072Numbers that are the sum of 3 positive cubesquadratic form22.0 %
A003136Loeschian numbers: numbers of the form x^2 + xy + y^2; norms of vectors in A2 latticequadratic form24.2 %
A003151Beatty sequence for 1+sqrt(2); a(n) = floor(n*(1+sqrt(2)))Beatty14.9 %
A003152A Beatty sequence: a(n) = floor(n*(1+1/sqrt(2)))Beatty12.5 %
A003154Centered 12-gonal numbers, or centered dodecagonal numbers: numbers of the form 6*k*(k-1) + 1polynomial100.0 %
A003159Numbers whose binary representation ends in an even number of zerosbinary rule13.9 %
A003185a(n) = (4*n+1)*(4*n+5)polynomial100.0 %
A003215Hex (or centered hexagonal) numbers: 3*n*(n+1)+1 (crystal ball sequence for hexagonal lattice)polynomial100.0 %
A003219Self numbers divisible by sum of their digits (or, self numbers which are also Harshad numbers)digit rule33.2 %
A003231a(n) = floor(n*(sqrt(5)+5)/2)Beatty17.7 %
A003277Cyclic numbers: k such that k and phi(k) are relatively prime; also k such that there is just one group of order k, i.e., A000001(k) = 1divisor functions15.1 %
A003278Szekeres's sequence: a(n)-1 in ternary = n-1 in binary; also: a(1) = 1, a(2) = 2, and thereafter a(n) is smallest number k which avoids any 3-term arithmetic progression in a(1), a(2), ..., a(n-1), kdigit rule0.4 %
A003309Ludic numbers: apply the same sieve as Eratosthenes, but cross off every k-th remaining numbersieve27.2 %
A003325Numbers that are the sum of 2 positive cubesquadratic form50.1 %
A003485Hurwitz-Radon function at powers of 2powers4.5 %
A003511A Beatty sequence: floor( n * (1 + sqrt(3))/2 )Beatty11.3 %
A003512A Beatty sequence: floor(n*(sqrt(3) + 2))Beatty18.0 %
A003600Maximal number of pieces obtained by slicing a torus (or a bagel) with n cuts: (n^3 + 3*n^2 + 8*n)/6 (n > 0)polynomial100.0 %
A003601Numbers j such that the average of the divisors of j is an integer: sigma_0(j) divides sigma_1(j). Alternatively, numbers j such that tau(j) (A000005(j)) divides sigma(j) (A000203(j))divisor functions11.9 %
A003607Location of 0's when natural numbers are listed in binarybinary rule12.9 %
A003622The Wythoff compound sequence AA: a(n) = floor(n*phi^2) - 1, where phi = (1+sqrt(5))/2Beatty15.5 %
A003623Wythoff AB-numbers: floor(floor(n*phi^2)*phi), where phi = (1+sqrt(5))/2Beatty18.6 %
A003625Primes congruent to {3, 5, 6} mod 7primes23.7 %
A003626Inert rational primes in Q(sqrt(-5))primes27.8 %
A003628Primes congruent to {5, 7} mod 8primes28.0 %
A003629Primes p == +- 3 (mod 8), or, primes p such that 2 is not a square mod pprimes28.0 %
A003631Primes congruent to 2 or 3 modulo 5primes32.2 %
A003635Inconsummate numbers in base 10: no number is this multiple of the sum of its digits (in base 10)digit rule18.0 %
A003714Fibbinary numbers: if n = F(i1) + F(i2) + ... + F(ik) is the Zeckendorf representation of n (i.e., write n in Fibonacci number system) then a(n) = 2^(i1 - 2) + 2^(i2 - 2) + ... + 2^(ik - 2). Also numbers whose binary representation contains no two adjacent 1'sbinary rule10.4 %
A003726Numbers with no 3 adjacent 1's in binary expansionbinary rule9.9 %
A003754Numbers with no adjacent 0's in binary expansionbinary rule11.6 %
A003777a(n) = n^3 + n^2 - 1polynomial100.0 %
A003796Numbers with no 3 adjacent 0's in binary expansionbinary rule10.6 %
A003814Numbers k such that the continued fraction for sqrt(k) has odd period lengthquadratic form19.1 %
A004006a(n) = C(n,1) + C(n,2) + C(n,3), or n*(n^2 + 5)/6polynomial100.0 %
A004126a(n) = n*(7*n^2 - 1)/6polynomial100.0 %
A004188a(n) = n*(3*n^2 - 1)/2polynomial100.0 %
A004201Accept one, reject one, accept two, reject two, ..block9.4 %
A004202Skip 1, take 1, skip 2, take 2, skip 3, take 3, etcblock9.3 %
A004207a(0) = 1, a(n) = sum of digits of all previous termsdigit rule14.2 %
A004214Positive numbers that are not the sum of three nonzero squaresquadratic form23.7 %
A004215Numbers that are the sum of 4 but no fewer nonzero squaresquadratic form23.7 %
A004431Numbers that are the sum of 2 distinct nonzero squaresquadratic form16.0 %
A004432Numbers that are the sum of 3 distinct nonzero squaresquadratic form8.6 %
A004433Numbers that are the sum of 4 distinct nonzero squares: of form w^2+x^2+y^2+z^2 with 0<w<x<y<zquadratic form9.6 %
A004466a(n) = n*(5*n^2 - 2)/3polynomial100.0 %
A004467a(n) = n*(11*n^2 - 5)/6polynomial100.0 %
A004611Divisible only by primes congruent to 1 mod 3multiplicative32.6 %
A004614Numbers that are divisible only by primes congruent to 3 mod 4multiplicative23.6 %
A004678Primes written in base 4digit rule27.3 %
A004679Primes written in base 5digit rule27.6 %
A004680Primes written in base 6digit rule30.7 %
A004681Primes written in base 7digit rule23.6 %
A004682Primes written in base 8digit rule30.8 %
A004683Primes written in base 9digit rule24.6 %
A004709Cubefree numbers: numbers that are not divisible by any cube > 1multiplicative10.2 %
A004742Numbers whose binary expansion does not contain 101binary rule13.6 %
A004743Numbers whose binary expansion does not contain 110binary rule11.4 %
A004744Numbers whose binary expansion does not contain 011binary rule11.3 %
A004745Numbers whose binary expansion does not contain 001binary rule10.1 %
A004746Numbers whose binary expansion does not contain 010binary rule12.1 %
A004767a(n) = 4*n + 3arithmetic progression23.2 %
A004780Binary expansion contains 2 adjacent 1'sbinary rule9.7 %
A004919a(n) = floor(n*phi^4), where phi is the golden ratio, A001622Beatty22.3 %
A004920a(n) = floor(n*phi^5), where phi is the golden ratio, A001622Beatty25.8 %
A004921a(n) = floor(n*phi^6), phi = golden ratio, A001622Beatty29.2 %
A004922a(n) = floor(n*phi^7), where phi is the golden ratio, A001622Beatty32.4 %
A004976a(n) = floor(n*phi^3), where phi=(1+sqrt(5))/2Beatty18.9 %
A004999Sums of two nonnegative cubesquadratic form49.9 %
A005097(Odd primes - 1)/2primes22.4 %
A005098Numbers k such that 4k + 1 is primeprime values22.8 %
A005100Deficient numbers: numbers k such that sigma(k) < 2kdivisor functions7.8 %
A005101Abundant numbers (sum of divisors of m exceeds 2m)divisor functions14.9 %
A005117Squarefree numbers: numbers that are not divisible by a square greater than 1multiplicative10.7 %
A005122Numbers k such that 8k - 1 is primeprime values22.8 %
A005123Numbers k such that 8k + 1 is primeprime values22.9 %
A005124Numbers k such that 8k + 3 is primeprime values15.8 %
A005125Numbers k such that 8k - 3 is primeprime values17.4 %
A005153Practical numbers: positive integers m such that every k <= sigma(m) is a sum of distinct divisors of m. Also called panarithmic numbersdivisor functions17.5 %
A005187a(n) = a(floor(n/2)) + n; also denominators in expansion of 1/sqrt(1-x) are 2^a(n); also 2n - number of 1's in binary expansion of 2nsummatory12.5 %
A005214Triangular numbers together with squares (excluding 0)polynomial83.8 %
A005228Sequence and first differences (A030124) together list all positive numbers exactly onceself-referential100.0 %
A005236Barriers for omega(n): numbers n such that, for all m < n, m + omega(m) <= nself-referential33.1 %
A005237Numbers k such that k and k+1 have the same number of divisorsdivisor functions21.9 %
A005238Numbers k such that k, k+1 and k+2 have the same number of divisorsmultiplicative36.7 %
A005244A self-generating sequence: start with 2 and 3, take all products of any 2 previous elements, subtract 1 and adjoin them to the sequenceself-referential22.2 %
A005277Nontotients: even numbers k such that phi(m) = k has no solutiondivisor functions10.7 %
A005279Numbers having divisors d, e with d < e < 2*ddivisor functions15.2 %
A005286a(n) = (n + 3)*(n^2 + 6*n + 2)/6polynomial100.0 %
A005349Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digitsdigit rule20.3 %
A005381Numbers k such that k and k-1 are compositecomplement2.5 %
A005382Primes p such that 2p-1 is also primeprimes47.8 %
A005383Primes p such that (p+1)/2 is primeprimes52.2 %
A005384Sophie Germain primes p: 2p+1 is also primeprimes47.3 %
A005385Safe primes p: (p-1)/2 is also primeprimes52.0 %
A005408The odd numbers: a(n) = 2*n + 1forced divisor18.0 %
A005448Centered triangular numbers: a(n) = 3*n*(n-1)/2 + 1polynomial100.0 %
A005449Second pentagonal numbers: a(n) = n*(3*n + 1)/2polynomial100.0 %
A005473Primes of form k^2 + 4primes100.0 %
A005475a(n) = n*(5*n+1)/2polynomial100.0 %
A005476a(n) = n*(5*n - 1)/2polynomial100.0 %
A005491a(n) = n^3 + 3*n + 1polynomial100.0 %
A005563a(n) = n*(n+2) = (n+1)^2 - 1polynomial100.0 %
A005574Numbers k such that k^2 + 1 is primeprime values23.9 %
A005586a(n) = n*(n+4)*(n+5)/6polynomial100.0 %
A005598a(n) = 1 + Sum_{i=1..n} (n-i+1)*phi(i)divisor functions100.0 %
A005658If n appears so do 2n, 3n+2, 6n+3self-referential13.5 %
A005744Expansion of x*(1+x-x^2)/((1-x)^4*(1+x))polynomial100.0 %
A005836Numbers whose base-3 representation contains no 2digit rule14.7 %
A005843The nonnegative even numbers: a(n) = 2narithmetic progression9.6 %
A005846Primes of the form k^2 + k + 41primes100.0 %
A005891Centered pentagonal numbers: (5n^2+5n+2)/2; crystal ball sequence for 3.3.3.4.4. planar netpolynomial100.0 %
A005893Number of points on surface of tetrahedron; coordination sequence for sodalite net (equals 2*n^2+2 for n > 0)polynomial100.0 %
A005894Centered tetrahedral numberspolynomial100.0 %
A005897a(n) = 6*n^2 + 2 for n > 0, a(0)=1polynomial100.0 %
A005898Centered cube numbers: n^3 + (n+1)^3polynomial100.0 %
A005899Number of points on surface of octahedron; also coordination sequence for cubic lattice: a(0) = 1; for n > 0, a(n) = 4n^2 + 2polynomial100.0 %
A005900Octahedral numbers: a(n) = n*(2*n^2 + 1)/3polynomial100.0 %
A005901Number of points on surface of cuboctahedron (or icosahedron): a(0) = 1; for n > 0, a(n) = 10n^2 + 2. Also coordination sequence for f.c.c. or A_3 or D_3 latticepolynomial100.0 %
A005902Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. latticepolynomial100.0 %
A005906Truncated tetrahedral numbers: a(n) = (1/6)*(n+1)*(23*n^2 + 19*n + 6)polynomial100.0 %
A005914Number of points on surface of hexagonal prism: 12*n^2 + 2 for n > 0 (coordination sequence for W(2))polynomial100.0 %
A005915Hexagonal prism numbers: a(n) = (n + 1)*(3*n^2 + 3*n + 1)polynomial100.0 %
A005917Rhombic dodecahedral numbers: a(n) = n^4 - (n - 1)^4polynomial100.0 %
A005920Tricapped prism numberspolynomial100.0 %
A005993Expansion of (1+x^2)/((1-x)^2*(1-x^2)^2)polynomial100.0 %
A006000a(n) = (n+1)*(n^2+n+2)/2polynomial100.0 %
A006002a(n) = n*(n+1)^2/2polynomial100.0 %
A006003a(n) = n*(n^2 + 1)/2polynomial100.0 %
A006004a(n) = C(n+2,3) + C(n,3) + C(n-1,3)polynomial100.0 %
A006046Total number of odd entries in first n rows of Pascal's triangle: a(0) = 0, a(1) = 1, a(2k) = 3*a(k), a(2k+1) = 2*a(k) + a(k+1). a(n) = Sum_{i=0..n-1} 2^wt(i)summatory55.2 %
A006049Numbers k such that k and k+1 have the same number of distinct prime divisorsmultiplicative16.7 %
A006073Numbers k such that k, k+1 and k+2 all have the same number of distinct prime divisorsmultiplicative22.0 %
A006093a(n) = prime(n) - 1primes22.4 %
A006094Products of 2 successive primesprimes100.0 %
A006218a(n) = Sum_{k=1..n} floor(n/k); also Sum_{k=1..n} d(k), where d = number of divisors (A000005); also number of solutions to x*y = z with 1 <= x,y,z <= nsummatory23.4 %
A006222a(n) = 11*n^2 + 11*n + 3polynomial100.0 %
A006254Numbers k such that 2k-1 is primeprimes22.3 %
A006285Odd numbers not of form p + 2^k (de Polignac numbers)primes29.7 %
A006331a(n) = n*(n+1)*(2*n+1)/3polynomial100.0 %
A006364Numbers k with an even number of 1's in binary, ignoring last bitbinary rule13.1 %
A006378Prime self (or Colombian) numbers: primes not expressible as the sum of an integer and its digit sumprimes41.7 %
A006446Numbers k such that floor(sqrt(k)) divides kblock70.0 %
A006450Prime-indexed primes: primes with prime subscriptsprimes43.3 %
A006489Numbers k such that k-6, k, and k+6 are primesprimes60.5 %
A006503a(n) = n*(n+1)*(n+8)/6polynomial100.0 %
A006507a(n+1) = a(n) + sum of digits of a(n), with a(1)=7digit rule14.2 %
A006512Greater of twin primesprimes46.9 %
A006527a(n) = (n^3 + 2*n)/3polynomial100.0 %
A006532Numbers whose sum of divisors is a squaredivisor functions45.4 %
A006562Balanced primes (of order one): primes which are the average of the previous prime and the following primeprimes52.4 %
A006564Icosahedral numbers: a(n) = n*(5*n^2 - 5*n + 2)/2polynomial100.0 %
A006566Dodecahedral numbers: a(n) = n*(3*n - 1)*(3*n - 2)/2polynomial100.0 %
A006567Emirps (primes whose reversal is a different prime)primes31.5 %
A006597a(n) = n^2*(5*n-3)/2polynomial100.0 %
A006753Smith (or joke) numbers: composite numbers k such that sum of digits of k = sum of digits of prime factors of k (counted with multiplicity)digit rule29.2 %
A006881Squarefree semiprimes: Numbers that are the product of two distinct primesmultiplicative15.7 %
A006918a(n) = binomial(n+3, 3)/4 for odd n, n*(n+2)*(n+4)/24 for even npolynomial100.0 %
A006995Binary palindromes: numbers whose binary expansion is palindromicbinary rule88.4 %
A007064Numbers not of form "nearest integer to n*tau", tau = (1+sqrt(5))/2Beatty15.4 %
A007066a(n) = 1 + ceiling((n-1)*phi^2), phi = (1+sqrt(5))/2Beatty15.5 %
A007088The binary numbers (or binary words, or binary vectors, or binary expansion of n): numbers written in base 2binary rule12.7 %
A007089Numbers in base 3digit rule10.7 %
A007090Numbers in base 4digit rule12.7 %
A007091Numbers in base 5digit rule11.1 %
A007092Numbers in base 6digit rule10.6 %
A007093Numbers in base 7digit rule11.8 %
A007094Numbers in base 8digit rule10.0 %
A007095Numbers in base 9digit rule9.2 %
A007202Crystal ball sequence for hexagonal close-packingpolynomial100.0 %
A007304Sphenic numbers: products of 3 distinct primesmultiplicative17.0 %
A007310Numbers congruent to 1 or 5 mod 6forced divisor9.6 %
A007378a(n), for n >= 2, is smallest positive integer which is consistent with sequence being monotonically increasing and satisfying a(a(n)) = 2nself-referential9.5 %
A007412The noncubes: a(n) = n + floor((n + floor(n^(1/3)))^(1/3))complement9.6 %
A007491Smallest prime > n^2primes100.0 %
A007494Numbers that are congruent to 0 or 2 mod 3residue class17.5 %
A007500Primes whose reversal in base 10 is also prime (called "palindromic primes" by David Wells, although that name usually refers to A002385). Also called reversible primesprimes31.5 %
A007504Sum of the first n primessummatory100.0 %
A007510Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is primeprimes26.1 %
A007519Primes of form 8n+1, that is, primes congruent to 1 mod 8primes33.3 %
A007520Primes == 3 (mod 8)primes33.3 %
A007521Primes of the form 8k + 5primes33.3 %
A007522Primes of the form 8*k+7, that is, primes congruent to -1 mod 8primes33.1 %
A007528Primes of the form 6k-1primes35.2 %
A007529Prime triples: p; p+2 or p+4; p+6 all primeprimes49.1 %
A007533a(n) = (5*n + 1)^2 + 4*n + 1polynomial100.0 %
A0075849-gonal (or enneagonal) pyramidal numbers: a(n) = n*(n+1)*(7*n-4)/6polynomial100.0 %
A00758510-gonal (or decagonal) pyramidal numbers: a(n) = n*(n + 1)*(8*n - 5)/6polynomial100.0 %
A00758611-gonal (or hendecagonal) pyramidal numbers: a(n) = n*(n+1)*(3*n-2)/2polynomial100.0 %
A00758712-gonal (or dodecagonal) pyramidal numbers: a(n) = n*(n+1)*(10*n-7)/6polynomial100.0 %
A007588Stella octangula numbers: a(n) = n*(2*n^2 - 1)polynomial100.0 %
A007590a(n) = floor(n^2/2)polynomial100.0 %
A007591Numbers k such that k^2 + 4 is primeprime values33.3 %
A007606Take 1, skip 2, take 3, etcblock9.3 %
A007612a(n+1) = a(n) + digital root (A010888) of a(n)digit rule0.0 %
A007617Values not in range of Euler phi functiondivisor functions11.1 %
A007618a(n) = a(n-1) + sum of digits of a(n-1), a(1) = 5digit rule14.2 %
A007635Primes of form n^2 + n + 17primes100.0 %
A007637Primes of form 3*k^2 - 3*k + 23primes100.0 %
A007639Primes of form 2n^2 - 2n + 19primes100.0 %
A007641Primes of the form 2*k^2 + 29primes100.0 %
A007674Numbers m such that m and m+1 are squarefreemultiplicative14.6 %
A007675Numbers m such that m, m+1 and m+2 are squarefreemultiplicative28.7 %
A007692Numbers that are the sum of 2 nonzero squares in 2 or more waysquadratic form20.0 %
A007693Primes p such that 6*p + 1 is also primeprimes37.1 %
A007700Numbers n such that n, 2n+1, and 4n+3 all primeprimes67.4 %
A007742a(n) = n*(4*n+1)polynomial100.0 %
A007770Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map (see A003132) includes 1digit rule19.7 %
A007774Numbers that are divisible by exactly 2 different primes; numbers n with omega(n) = A001221(n) = 2multiplicative13.2 %
A007775Numbers not divisible by 2, 3 or 5forced divisor13.6 %
A007821Primes p such that pi(p) is not primeprimes23.8 %
A007904Crystal ball sequence for diamondpolynomial100.0 %
A007916Numbers that are not perfect powerspowers9.7 %
A007921Numbers that are not the difference of two primesprimes18.6 %
A007928Numbers containing an even digitdigit rule9.3 %
A007931Numbers that contain only 1's and 2's. Nonempty binary strings of length n in lexicographic orderdigit rule11.1 %
A007932Numbers that contain only 1's, 2's and 3'sdigit rule10.7 %
A007950Binary sieve: delete every 2nd number, then every 4th, 8th, etcsieve21.2 %
A007951Ternary sieve: delete every 3rd number, then every 9th, 27th, etcsieve3.5 %
A007957Numbers that contain an odd digitdigit rule9.9 %
A00836411-rough numbers: not divisible by 2, 3, 5 or 7forced divisor14.7 %
A00836513-rough numbers: positive integers that have no prime factors less than 13forced divisor15.5 %
A008366Smallest prime factor is >= 17forced divisor16.2 %
A008412Coordination sequence for 4-dimensional cubic lattice (points on surface of 4-dimensional cross-polytope)polynomial100.0 %
A008577Crystal ball sequence for planar net 4.8.8polynomial100.0 %
A008580Crystal ball sequence for planar net 3.6.3.6polynomial100.0 %
A008585a(n) = 3*nforced divisor9.6 %
A008586Multiples of 4arithmetic progression9.6 %
A008587Multiples of 5: a(n) = 5 * narithmetic progression9.6 %
A008588Nonnegative multiples of 6arithmetic progression9.6 %
A008589Multiples of 7arithmetic progression9.6 %
A008590Multiples of 8residue class9.6 %
A008593Multiples of 11residue class9.6 %
A008594Multiples of 12residue class9.6 %
A008595Multiples of 13residue class9.6 %
A008596Multiples of 14residue class9.6 %
A008597Multiples of 15residue class9.6 %
A008598Multiples of 16residue class9.6 %
A008599Multiples of 17residue class9.6 %
A008600Multiples of 18residue class9.6 %
A008601Multiples of 19residue class9.6 %
A008602Multiples of 20residue class9.6 %
A008603Multiples of 21residue class9.6 %
A008604Multiples of 22residue class9.6 %
A008605Multiples of 23residue class9.7 %
A008606Multiples of 24residue class9.6 %
A008607Multiples of 25residue class9.6 %
A008804Expansion of 1/((1-x)^2*(1-x^2)*(1-x^4))polynomial100.0 %
A008810a(n) = ceiling(n^2/3)polynomial100.0 %
A008846Hypotenuses of primitive Pythagorean trianglesmultiplicative23.8 %
A008851Congruent to 0 or 1 mod 5residue class17.6 %
A008854Numbers that are congruent to {0, 1, 4} mod 5residue class14.9 %
A008864a(n) = prime(n) + 1primes22.3 %
A008865a(n) = n^2 - 2polynomial100.0 %
A008917Numbers that are the sum of 3 positive cubes in more than one wayquadratic form34.5 %
A009112Areas of Pythagorean triangles: numbers which can be the area of a right triangle with integer sidesquadratic form48.3 %
A009177Numbers that are the hypotenuses of more than one Pythagorean trianglequadratic form16.5 %
A009440a(n) is the concatenation of n and 6ndigit rule100.0 %
A009441a(n) is the concatenation of n and 7ndigit rule100.0 %
A009470a(n) is the concatenation of n and 8ndigit rule100.0 %
A009474a(n) is the concatenation of n and 9ndigit rule100.0 %
A009994Numbers with digits in nondecreasing orderdigit rule19.8 %
A009996Numbers with digits in nonincreasing orderdigit rule17.2 %
A010061Binary self or Colombian numbers: numbers that cannot be expressed as the sum of distinct terms of the form 2^k+1 (k>=0), or equivalently, numbers not of form m + sum of binary digits of mbinary rule17.1 %
A010062a(0)=1; thereafter a(n+1) = a(n) + number of 1's in binary representation of a(n)digit rule23.9 %
A010063a(n+1) = a(n) + sum of digits in base 3 representation of a(n), with a(0) = 1digit rule22.3 %
A010064Base 4 self or Colombian numbers (not of form k + sum of base 4 digits of k)digit rule19.2 %
A010065a(n+1) = a(n) + sum of digits in base 4 representation of a(n), with a(0) = 1digit rule18.3 %
A010066a(n+1) = a(n) + sum of digits in base 5 representation of a(n)digit rule19.9 %
A010067Base 6 self or Colombian numbers (not of form k + sum of base 6 digits of k)digit rule20.8 %
A010068a(n+1) = a(n) + sum of digits in base 6 representation of a(n)digit rule16.9 %
A010069a(n+1) = a(n) + sum of digits in base 7 representation of a(n)digit rule15.9 %
A010070Base 8 self or Colombian numbers (not of form k + sum of base 8 digits of k)digit rule22.9 %
A010071a(n+1) = a(n) + sum of digits in base 8 representation of a(n)digit rule15.9 %
A010072a(n+1) = a(n) + sum of digits in base 9 representation of a(n)digit rule17.8 %
A011199a(n) = (n+1)*(2*n+1)*(3*n+1)polynomial100.0 %
A011379a(n) = n^2*(n+1)polynomial100.0 %
A011531Numbers that contain a digit 1 in their decimal representationdigit rule11.1 %
A011532Numbers that contain a 2digit rule11.4 %
A011533Numbers that contain a 3digit rule12.7 %
A011534Numbers that contain a 4digit rule11.5 %
A011535Numbers that contain a 5digit rule10.8 %
A011536Numbers that contain a 6digit rule12.0 %
A011537Numbers that contain at least one 7digit rule13.6 %
A011538Numbers that contain an 8digit rule11.2 %
A011539"9ish numbers": decimal representation contains at least one ninedigit rule13.6 %
A011540Numbers that contain a digit 0digit rule8.8 %
A013656a(n) = n*(9*n-2)polynomial100.0 %
A013916Numbers k such that the sum of the first k primes is primeprimes24.1 %
A013917a(n) is prime and sum of all primes <= a(n) is primeprimes47.8 %
A013929Numbers that are not squarefree. Numbers that are divisible by a square greater than 1. The complement of A005117multiplicative13.0 %
A013939Partial sums of sequence A001221 (number of distinct primes dividing n)summatory15.3 %
A014076Odd nonprimescomplement21.0 %
A014091Numbers that are the sum of 2 primesprimes22.6 %
A014092Numbers that are not the sum of 2 primesprimes4.2 %
A014105Second hexagonal numbers: a(n) = n*(2*n + 1)polynomial100.0 %
A014106a(n) = n*(2*n + 3)polynomial100.0 %
A014132Complement of triangular numbers (A000217); also array T(n,k) = ((n+k)^2 + n-k)/2, n, k > 0, read by antidiagonalscomplement9.5 %
A014190Palindromes in base 3 (written in base 10)digit rule84.2 %
A014192Palindromes in base 4 (written in base 10)digit rule83.2 %
A014206a(n) = n^2 + n + 2polynomial100.0 %
A014261Numbers that contain odd digits onlydigit rule17.4 %
A014263Numbers that contain even digits onlydigit rule11.1 %
A014312Numbers with exactly 4 ones in binary expansionbinary rule12.9 %
A014313Numbers with exactly 5 ones in binary expansionbinary rule8.9 %
A014439Differences between two positive cubes in exactly 1 waypowers44.3 %
A014567Numbers k such that k and sigma(k) are relatively prime, where sigma(k) = sum of divisors of k (A000203)multiplicative13.5 %
A014574Average of twin prime pairsprimes31.8 %
A014601Numbers congruent to 0 or 3 mod 4residue class12.3 %
A014612Numbers that are the product of exactly three (not necessarily distinct) primesmultiplicative15.8 %
A014613Numbers that are products of 4 primesmultiplicative16.9 %
A014614Numbers that are products of 5 primes (or 5-almost primes, a generalization of semiprimes)multiplicative18.0 %
A014634a(n) = (2*n+1)*(4*n+1)polynomial100.0 %
A014635a(n) = 2*n*(4*n - 1)polynomial100.0 %
A014657Numbers m that divide 2^k + 1 for some nonnegative kmultiplicative23.6 %
A014661Numbers that do not divide 2^k + 1 for any k>0multiplicative11.2 %
A014688a(n) = n-th prime + nprimes25.3 %
A014752Primes of the form x^2 + 27y^2quadratic form42.3 %
A015237a(n) = (2*n - 1)*n^2polynomial100.0 %
A015614a(n) = -1 + Sum_{i=1..n} phi(i)summatory93.3 %
A015911Numbers k such that 2^k mod k is oddpowers24.4 %
A015976One iteration of Reverse and Add is needed to reach a palindromedigit rule10.7 %
A015977Two iterations of Reverse and Add are needed to reach a palindromedigit rule13.0 %
A015979Three iterations of Reverse and Add are needed to reach a palindromedigit rule16.2 %
A015980Four iterations of Reverse and Add are needed to reach a palindromedigit rule20.4 %
A015982Five iterations of Reverse and Add are needed to reach a palindromedigit rule21.0 %
A015984Six iterations of Reverse and Add are needed to reach a palindromedigit rule23.8 %
A016038Strictly non-palindromic numbers: n is not palindromic in any base b with 2 <= b <= n-2digit rule43.1 %
A016052a(1) = 3; for n >= 1, a(n+1) = a(n) + sum of its digitsdigit rule14.7 %
A016061a(n) = n*(n+1)*(4*n+5)/6polynomial100.0 %
A016096a(n+1) = a(n) + sum of its digits, with a(1) = 9digit rule17.4 %
A016105Blum integers: numbers of the form p * q where p and q are distinct primes congruent to 3 (mod 4)multiplicative29.9 %
A016754Odd squares: a(n) = (2n+1)^2. Also centered octagonal numberspolynomial100.0 %
A016766a(n) = (3*n)^2polynomial100.0 %
A016777a(n) = 3*n + 1arithmetic progression19.9 %
A016778a(n) = (3*n+1)^2polynomial100.0 %
A016789a(n) = 3*n + 2arithmetic progression19.9 %
A016790a(n) = (3n+2)^2polynomial100.0 %
A016802a(n) = (4*n)^2polynomial100.0 %
A016813a(n) = 4*n + 1arithmetic progression23.2 %
A016814a(n) = (4*n + 1)^2polynomial100.0 %
A016825Positive integers congruent to 2 (mod 4): a(n) = 4*n+2, for n >= 0residue class18.0 %
A016826a(n) = (4n + 2)^2polynomial100.0 %
A016838a(n) = (4*n + 3)^2polynomial100.0 %
A016850a(n) = (5*n)^2polynomial100.0 %
A016862a(n) = (5*n + 1)^2polynomial100.0 %
A016874a(n) = (5*n + 2)^2polynomial100.0 %
A016885a(n) = 5*n + 3arithmetic progression22.6 %
A016886a(n) = (5*n + 3)^2polynomial100.0 %
A016898a(n) = (5*n + 4)^2polynomial100.0 %
A016910a(n) = (6*n)^2polynomial100.0 %
A016922a(n) = (6*n + 1)^2polynomial100.0 %
A016934a(n) = (6*n + 2)^2polynomial100.0 %
A016946a(n) = (6*n+3)^2polynomial100.0 %
A016958a(n) = (6*n + 4)^2polynomial100.0 %
A016970a(n) = (6*n + 5)^2polynomial100.0 %
A016982a(n) = (7*n)^2polynomial100.0 %
A016994a(n) = (7*n + 1)^2polynomial100.0 %
A017006a(n) = (7*n+2)^2polynomial100.0 %
A017018a(n) = (7*n + 3)^2polynomial100.0 %
A017030a(n) = (7*n + 4)^2polynomial100.0 %
A017042a(n) = (7*n + 5)^2polynomial100.0 %
A017054a(n) = (7*n + 6)^2polynomial100.0 %
A017066a(n) = (8*n)^2polynomial100.0 %
A017078a(n) = (8*n + 1)^2polynomial100.0 %
A017090a(n) = (8*n + 2)^2polynomial100.0 %
A017102a(n) = (8n + 3)^2polynomial100.0 %
A017114a(n) = (8*n + 4)^2polynomial100.0 %
A017126a(n) = (8*n + 5)^2polynomial100.0 %
A017138a(n) = (8*n+6)^2polynomial100.0 %
A017150a(n) = (8*n + 7)^2polynomial100.0 %
A017162a(n) = (9*n)^2polynomial100.0 %
A017174a(n) = (9*n + 1)^2polynomial100.0 %
A017186a(n) = (9*n + 2)^2polynomial100.0 %
A017198a(n) = (9*n + 3)^2polynomial100.0 %
A017210a(n) = (9*n + 4)^2polynomial100.0 %
A017222a(n) = (9*n + 5)^2polynomial100.0 %
A017234a(n) = (9*n + 6)^2polynomial100.0 %
A017246a(n) = (9*n + 7)^2polynomial100.0 %
A017258a(n) = (9*n + 8)^2polynomial100.0 %
A017270a(n) = (10*n)^2polynomial100.0 %
A017282a(n) = (10*n + 1)^2polynomial100.0 %
A017294a(n) = (10*n + 2)^2polynomial100.0 %
A017306a(n) = (10*n + 3)^2polynomial100.0 %
A017318a(n) = (10*n + 4)^2polynomial100.0 %
A017330a(n) = (10*n + 5)^2polynomial100.0 %
A017342a(n) = (10*n + 6)^2polynomial100.0 %
A017354a(n) = (10*n + 7)^2polynomial100.0 %
A017366a(n) = (10*n + 8)^2polynomial100.0 %
A017378a(n) = (10*n + 9)^2polynomial100.0 %
A017390a(n) = (11*n)^2polynomial100.0 %
A017402a(n) = (11*n+1)^2polynomial100.0 %
A017414a(n) = (11*n + 2)^2polynomial100.0 %
A017426a(n) = (11*n + 3)^2polynomial100.0 %
A017438a(n) = (11*n + 4)^2polynomial100.0 %
A017450a(n) = (11*n + 5)^2polynomial100.0 %
A017462a(n) = (11*n + 6)^2polynomial100.0 %
A017474a(n) = (11*n + 7)^2polynomial100.0 %
A017486a(n) = (11*n + 8)^2polynomial100.0 %
A017498a(n) = (11*n + 9)^2polynomial100.0 %
A017510a(n) = (11*n + 10)^2polynomial100.0 %
A017522a(n) = (12*n)^2polynomial100.0 %
A017534a(n) = (12*n + 1)^2polynomial100.0 %
A017546a(n) = (12*n + 2)^2polynomial100.0 %
A017558a(n) = (12*n + 3)^2polynomial100.0 %
A017570a(n) = (12*n + 4)^2polynomial100.0 %
A017582a(n) = (12*n + 5)^2polynomial100.0 %
A017594a(n) = (12*n + 6)^2polynomial100.0 %
A017606a(n) = (12*n + 7)^2polynomial100.0 %
A017618a(n) = (12*n + 8)^2polynomial100.0 %
A017630a(n) = (12*n + 9)^2polynomial100.0 %
A017642a(n) = (12*n+10)^2polynomial100.0 %
A017654a(n) = (12*n + 11)^2polynomial100.0 %
A018805Number of elements in the set {(x,y): 1 <= x,y <= n, gcd(x,y)=1}summatory98.0 %
A018825Numbers that are not the sum of 2 nonzero squarescomplement13.5 %
A019298Number of balls in pyramid with base either a regular hexagon or a hexagon with alternate sides differing by 1 (balls in hexagonal pyramid of height n taken from hexagonal close-packing)polynomial100.0 %
A019506Hoax numbers: composite numbers whose digit-sum equals the sum of the digit-sums of its distinct prime factorsdigit rule27.5 %
A019546Primes whose digits are primes; primes having only {2, 3, 5, 7} as digitsprimes34.2 %
A019550a(n) is the concatenation of n and 2ndigit rule100.0 %
A019551a(n) is the concatenation of n and 3ndigit rule100.0 %
A019552a(n) is the concatenation of n and 4ndigit rule100.0 %
A019553a(n) is the concatenation of n and 5ndigit rule100.0 %
A020668Numbers of the form x^2 + 4*y^2quadratic form20.2 %
A020669Numbers of form x^2 + 5 y^2quadratic form22.9 %
A020670Numbers of form x^2 + 7y^2quadratic form17.3 %
A020671Numbers of form x^2 + 8 y^2quadratic form20.4 %
A020672Numbers of form x^2 + 9 y^2quadratic form24.5 %
A020673Numbers of form x^2 + 10 y^2quadratic form21.5 %
A020674Numbers of the form 2*x^2 + 5*y^2quadratic form20.7 %
A020675Numbers of form 2 x^2 + 7 y^2quadratic form17.6 %
A020676Numbers of form 2 x^2 + 9 y^2quadratic form23.1 %
A020677Numbers of form 3*x^2 + 4*y^2quadratic form25.3 %
A020678Numbers of form 3 x^2 + 5 y^2quadratic form30.5 %
A020679Numbers of form 3*x^2 + 7*y^2quadratic form24.0 %
A020680Numbers of form 3 x^2 + 8 y^2quadratic form26.5 %
A020681Numbers of form 3 x^2 + 10 y^2quadratic form28.7 %
A020682Numbers of form 4 x^2 + 5 y^2quadratic form27.7 %
A020683Numbers of form 4 x^2 + 7 y^2quadratic form17.9 %
A020684Numbers of form 4 x^2 + 9 y^2quadratic form29.9 %
A020685Numbers of form 5 x^2 + 6 y^2quadratic form28.8 %
A020686Numbers of form 5 x^2 + 7 y^2quadratic form25.8 %
A020687Numbers of form 5 x^2 + 8 y^2quadratic form26.9 %
A020688Numbers of form 5 x^2 + 9 y^2quadratic form31.7 %
A020689Numbers of form 6 x^2 + 7 y^2quadratic form23.2 %
A020690Numbers of form 7 x^2 + 8 y^2quadratic form22.7 %
A020691Numbers of form 7 x^2 + 9 y^2quadratic form27.3 %
A020692Numbers of form 7 x^2 + 10 y^2quadratic form22.6 %
A020693Numbers of the form 8*x^2 + 9*y^2quadratic form28.7 %
A020694Numbers of form 9 x^2 + 10 y^2quadratic form32.5 %
A020756Numbers that are the sum of two triangular numbersquadratic form14.8 %
A020757Numbers that are not the sum of two triangular numbersquadratic form12.3 %
A020893Squarefree sums of two squares; or squarefree numbers with no prime factors of the form 4k+3quadratic form17.3 %
A020899Numbers k with an odd number of terms in their Zeckendorf representation (write k as a sum of non-consecutive distinct Fibonacci numbers)digit rule13.0 %
A022004Initial members of prime triples (p, p+2, p+6)primes63.4 %
A022005Initial members of prime triples (p, p+4, p+6)primes66.2 %
A022155Values of n at which Golay-Rudin-Shapiro sequence A020985 is negativebinary rule11.5 %
A022264a(n) = n*(7*n - 1)/2polynomial100.0 %
A022265a(n) = n*(7*n + 1)/2polynomial100.0 %
A022266a(n) = n*(9*n - 1)/2polynomial100.0 %
A022267a(n) = n*(9*n + 1)/2polynomial100.0 %
A022268a(n) = n*(11*n - 1)/2polynomial100.0 %
A022269a(n) = n*(11*n+1)/2polynomial100.0 %
A022270a(n) = n*(13*n - 1)/2polynomial100.0 %
A022271a(n) = n*(13*n + 1)/2polynomial100.0 %
A022272a(n) = n*(15*n - 1)/2polynomial100.0 %
A022273a(n) = n*(15*n + 1)/2polynomial100.0 %
A022274a(n) = n*(17*n - 1)/2polynomial100.0 %
A022275a(n) = n*(17*n + 1)/2polynomial100.0 %
A022276a(n) = n*(19*n - 1)/2polynomial100.0 %
A022277a(n) = n*(19*n + 1)/2polynomial100.0 %
A022278a(n) = n*(21*n-1)/2polynomial100.0 %
A022279a(n) = n*(21*n + 1)/2polynomial100.0 %
A022280a(n) = n*(23*n - 1)/2polynomial100.0 %
A022281a(n) = n*(23*n + 1)/2polynomial100.0 %
A022282a(n) = n*(25*n - 1)/2polynomial100.0 %
A022283a(n) = n*(25*n + 1)/2polynomial100.0 %
A022284a(n) = n*(27*n - 1)/2polynomial100.0 %
A022285a(n) = n*(27*n + 1)/2polynomial100.0 %
A022286a(n) = n*(29*n - 1)/2polynomial100.0 %
A022287a(n) = n*(29*n + 1)/2polynomial100.0 %
A022288a(n) = n*(31*n-1)/2polynomial100.0 %
A022289a(n) = n*(31*n + 1)/2polynomial100.0 %
A022342Integers with "even" Zeckendorf expansions (do not end with ... + F_2 = ... + 1) (the Fibonacci-even numbers); also, apart from first term, a(n) = Fibonacci successor to n-1Beatty12.3 %
A022449c(p(n)) where p(k) is k-th prime including p(1)=1 and c(k) is k-th composite numbercomplement24.6 %
A022544Numbers that are not the sum of 2 squaresquadratic form13.4 %
A022549Sum of a square and a nonnegative cubepowers24.8 %
A022559Sum of exponents in prime-power factorization of n!summatory16.6 %
A022797a(n) = n-th prime + n-th nonprimeprimes26.1 %
A022838Beatty sequence for sqrt(3); complement of A054406Beatty12.7 %
A022839Beatty sequence for sqrt(5)Beatty14.4 %
A022840Beatty sequence for sqrt(6)Beatty15.1 %
A022841Beatty sequence for sqrt(7)Beatty15.6 %
A022842Beatty sequence for sqrt(8)Beatty16.0 %
A022843Beatty sequence for e: a(n) = floor(n*e)Beatty15.7 %
A022844a(n) = floor(n*Pi)Beatty16.8 %
A022846Nearest integer to n*sqrt(2)Beatty11.3 %
A022847Integer nearest n*sqrt(3)Beatty12.7 %
A022848Integer nearest nx, where x = sqrt(5)Beatty14.5 %
A023173Numbers k such that Fibonacci(k) == 1 (mod k)self-referential19.6 %
A023197Numbers k such that sigma(k) >= 3*kdivisor functions16.8 %
A023200Primes p such that p + 4 is also primeprimes46.8 %
A023201Primes p such that p + 6 is also prime. (Lesser of a pair of sexy primes.)primes34.6 %
A023202Primes p such that p + 8 is also primeprimes47.0 %
A023203Primes p such that p + 10 is also primeprimes45.0 %
A023204Primes p such that 2*p + 3 is also primeprimes36.4 %
A023205Numbers m such that m and 2*m + 5 are both primeprimes44.8 %
A023208Primes p such that 3*p + 2 is also primeprimes36.4 %
A023209Primes p such that 3p + 4 is also primeprimes36.4 %
A023210Primes p such that 3*p + 8 is also primeprimes37.2 %
A023211Primes p such that 3*p + 10 is also primeprimes34.8 %
A023212Primes p such that 4*p+1 is also primeprimes47.6 %
A023213Primes p such that 4p + 3 is primeprimes37.2 %
A023214Primes p such that 4*p + 5 is also primeprimes45.4 %
A023215Primes p such that 4*p + 7 is also primeprimes46.0 %
A023216Primes p such that 4*p + 9 is also primeprimes37.5 %
A023217Primes p such that 5*p + 2 is also primeprimes45.2 %
A023218Primes p such that 5*p + 4 is also primeprimes45.5 %
A023219Primes p such that 5p+6 is a primeprimes34.5 %
A023220Primes p such that 5*p + 8 is also primeprimes45.4 %
A023221Primes p such that 6*p + 5 is also primeprimes34.9 %
A023222Primes p such that 6*p + 7 is also primeprimes36.2 %
A023223Primes p such that 7*p + 2 is also primeprimes46.7 %
A023224Primes p such that 7*p + 4 is also primeprimes47.1 %
A023225Primes p such that 7*p + 6 is also primeprimes35.4 %
A023226Primes p such that 7*p + 8 is also primeprimes46.5 %
A023227Primes p such that 7*p + 10 is also primeprimes44.2 %
A023229Primes p such that 8*p + 3 is also primeprimes37.7 %
A023231Primes p such that 8*p + 7 is also primeprimes46.6 %
A023232Primes p such that 8*p + 9 is also primeprimes36.7 %
A023233Primes p such that 9*p + 2 is also primeprimes37.4 %
A023234Primes p such that 9*p + 4 is also primeprimes37.7 %
A023235Primes p such that 9*p + 8 is also primeprimes37.7 %
A023236Primes p such that 9*p + 10 is also primeprimes34.8 %
A023237Primes p such that 10*p + 1 is also primeprimes45.7 %
A023238Primes p such that 10*p + 3 is also primeprimes34.9 %
A023239Primes p such that 10*p + 7 is also primeprimes44.5 %
A023240Primes p such that 10*p + 9 is also primeprimes35.1 %
A023241Primes that remain prime through 2 iterations of function f(x) = x + 6primes49.1 %
A023688Numbers with exactly 6 ones in binary expansionbinary rule8.9 %
A023689Numbers with exactly 7 ones in binary expansionbinary rule9.4 %
A023690Numbers with exactly 8 ones in binary expansionbinary rule11.4 %
A023691Numbers with exactly 9 ones in binary expansionbinary rule12.2 %
A023692Numbers with a single 1 in their ternary expansiondigit rule23.5 %
A023699Numbers with a single 2 in their ternary expansiondigit rule16.8 %
A023705Numbers with no 0's in base-4 expansiondigit rule12.2 %
A023706Numbers with a single 0 in their base 4 expansiondigit rule12.5 %
A023709Numbers with no 1's in their base 4 expansiondigit rule13.8 %
A023710Numbers with a single 1 in their base 4 expansiondigit rule15.9 %
A023713Numbers with no 2's in their base 4 expansiondigit rule14.2 %
A023714Numbers with a single 2 in their base 4 expansiondigit rule13.9 %
A023717Numbers with no 3's in base-4 expansiondigit rule7.8 %
A023718Numbers with a single 3 in their base 4 expansiondigit rule9.9 %
A023721Numbers with no 0's in their base-5 expansiondigit rule10.3 %
A023722Numbers with a single 0 in their base 5 expansiondigit rule10.6 %
A023725Numbers with no 1's in their base-5 expansiondigit rule13.0 %
A023726Numbers with a single 1 in their base 5 expansiondigit rule15.1 %
A023729Numbers with no 2's in their base-5 expansiondigit rule13.3 %
A023730Numbers with a single 2 in their base 5 expansiondigit rule15.0 %
A023733Numbers with no 3's in base-5 expansiondigit rule6.9 %
A023734Numbers with a single 3 in their base-5 expansiondigit rule8.1 %
A023738Numbers with a single 4 in their base 5 expansiondigit rule12.4 %
A024206Expansion of x^2*(1+x-x^2)/((1-x^2)*(1-x)^2)polynomial100.0 %
A024619Numbers that are not powers of primes p^k (k >= 0); complement of A000961complement10.6 %
A024675Average of two consecutive odd primesprimes24.9 %
A024892Numbers k such that 3*k+1 is primeprime values17.9 %
A024893Numbers k such that 3*k+2 is primeprime values25.9 %
A024894Numbers k such that 5*k + 1 is primeprime values21.5 %
A024895Numbers k such that 5*k - 3 is primeprime values14.6 %
A024896Numbers k such that 5*k - 2 is primeprime values30.1 %
A024897Numbers k such that 5*k + 4 is primeprime values29.9 %
A024898Positive integers k such that 6*k - 1 is primeprime values18.1 %
A024899Numbers k such that 6*k + 1 is primeprime values17.9 %
A024900Numbers k such that 7*k + 6 is primeprime values24.9 %
A024901Numbers k such that 7*k - 2 is primeprime values30.1 %
A024902Numbers k such that 7*k + 4 is primeprime values30.7 %
A024903Numbers k such that 7*k - 4 is primeprime values31.6 %
A024904Numbers k such that 7*k - 5 is primeprime values20.2 %
A024905Numbers k such that 7*k + 1 is primeprime values22.7 %
A024906Numbers k such that 9*k + 1 is primeprime values18.2 %
A024907Numbers k such that 9*k - 7 is primeprime values17.7 %
A024908Numbers k such that 9*k - 5 is primeprime values16.8 %
A024909Numbers k such that 9*k - 4 is primeprime values26.1 %
A024910Numbers k such that 9*k - 2 is primeprime values28.0 %
A024912Numbers k such that 10*k + 1 is primeprime values21.5 %
A024913Numbers k such that 10*k - 7 is primeprime values20.3 %
A024914Numbers k such that 10*k - 3 is primeprime values14.6 %
A024916a(n) = Sum_{k=1..n} k*floor(n/k); also Sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n (A000203)summatory100.0 %
A024974Numbers that are the sum of 3 distinct positive cubes in 2 or more wayspowers34.7 %
A024975Sums of three distinct positive cubespowers22.4 %
A025284Numbers that are the sum of 2 nonzero squares in exactly 1 wayquadratic form18.2 %
A025395Numbers that are the sum of 3 positive cubes in exactly 1 wayquadratic form22.9 %
A0254751 and the prime powers p^m where m >= 2, thus excluding the primespowers100.0 %
A025583Composite numbers that are not the sum of 2 primesmultiplicative5.4 %
A025584Primes p such that p-2 is not a primeprimes25.7 %
A026351a(n) = floor(n*phi) + 1, where phi = (1+sqrt(5))/2Beatty12.1 %
A026424Number of prime divisors (counted with multiplicity) is odd; Liouville function lambda(n) (A008836) is negativemultiplicative12.8 %
A026430a(n) is the sum of first n terms of A001285 (Thue-Morse sequence)binary rule17.5 %
A027444a(n) = n^3 + n^2 + npolynomial100.0 %
A027469a(n) = 49*(n-1)*(n-2)/2polynomial100.0 %
A027470a(n) = 225*(n-1)*(n-2)/2polynomial100.0 %
A027480a(n) = n*(n+1)*(n+2)/2polynomial100.0 %
A027575a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2polynomial100.0 %
A027602a(n) = n^3 + (n+1)^3 + (n+2)^3polynomial100.0 %
A027603a(n) = n^3 + (n+1)^3 + (n+2)^3 + (n+3)^3polynomial100.0 %
A027604a(n) = n^3 + (n+1)^3 + (n+2)^3 + (n+3)^3 + (n+4)^3polynomial100.0 %
A027620a(n) = n + (n+1)^2 + (n+2)^3polynomial100.0 %
A027688a(n) = n^2 + n + 3polynomial100.0 %
A027689a(n) = n^2 + n + 4polynomial100.0 %
A027690a(n) = n^2 + n + 5polynomial100.0 %
A027691a(n) = n^2 + n + 6polynomial100.0 %
A027692a(n) = n^2 + n + 7polynomial100.0 %
A027693a(n) = n^2 + n + 8polynomial100.0 %
A027694a(n) = n^2 + n + 9polynomial100.0 %
A027697Odious primes: primes with odd number of 1's in binary expansionprimes29.6 %
A027699Evil primes: primes with even number of 1's in their binary expansionprimes30.3 %
A027752Numbers k such that k^2 + k + 3 is primeprime values32.7 %
A027753Primes of form n^2 + n + 3primes100.0 %
A027754Numbers k such that k^2 + k + 5 is primeprime values24.6 %
A027755Primes of the form k^2 + k + 5primes100.0 %
A027756Numbers k such that k^2 + k + 7 is primeprime values24.1 %
A027757Numbers k such that k^2 + k + 9 is primeprime values33.4 %
A027758Primes of the form k^2 + k + 9primes100.0 %
A027849a(n) = (n+1)*(5*n^2+4*n+1)polynomial100.0 %
A027861Numbers k such that k^2 + (k+1)^2 is primeprime values22.3 %
A027862Primes of the form j^2 + (j+1)^2primes100.0 %
A027863Numbers k such that k^2 + (k+1)^2 + (k+2)^2 is primeprime values23.5 %
A027866Numbers k such that k^2 + (k+1)^2 + (k+2)^2 + (k+3)^2 + (k+4)^2 + (k+5)^2 is primeprime values21.4 %
A027867Primes of the form n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 + (n+5)^2primes100.0 %
A027903a(n) = n*(n + 1)*(3*n + 1)polynomial100.0 %
A028260Numbers with an even number of prime divisors (counted with multiplicity); numbers k such that the Liouville function lambda(k) (A008836) is positivemultiplicative12.8 %
A028347a(n) = n^2 - 4polynomial100.0 %
A028373Numbers that have only the straight digits {1, 4, 7}digit rule18.0 %
A028374Numbers that have only curved digits {0, 3, 6, 8, 9} or digits that are both curved and linear {2, 5}digit rule13.9 %
A028387a(n) = n + (n+1)^2polynomial100.0 %
A028552a(n) = n*(n+3)polynomial100.0 %
A028557a(n) = n*(n+5)polynomial100.0 %
A028560a(n) = n*(n + 6)polynomial100.0 %
A028563a(n) = n*(n+7)polynomial100.0 %
A028566a(n) = n*(n+8)polynomial100.0 %
A028569a(n) = n*(n + 9)polynomial100.0 %
A028823Numbers k such that k^2 + k + 17 is primeprime values18.7 %
A028834Numbers whose sum of digits is a primedigit rule10.7 %
A028835Numbers whose iterated sum of digits is a primedigit rule12.2 %
A028838Numbers whose sum of digits is a power of 2digit rule27.0 %
A028839Sum of digits of n is a squaredigit rule25.2 %
A028840Numbers k such that sum of digits of k is a Fibonacci numberdigit rule24.0 %
A028846Numbers whose product of digits is a power of 2digit rule5.2 %
A028870Numbers k such that k^2 - 2 is primeprime values30.1 %
A028871Primes of the form k^2 - 2primes100.0 %
A028872a(n) = n^2 - 3polynomial100.0 %
A028873Numbers k such that k^2 - 3 is primeprime values18.9 %
A028874Primes of form k^2 - 3primes100.0 %
A028876Numbers k such that k^2 - 5 is primeprime values19.3 %
A028877Primes of form k^2 - 5primes100.0 %
A028878a(n) = (n+3)^2 - 6polynomial100.0 %
A028879Numbers k such that k^2 - 6 is primeprime values31.6 %
A028880Primes of the form n^2 - 6primes100.0 %
A028881a(n) = n^2 - 7polynomial100.0 %
A028882Numbers k such that k^2 - 7 is primeprime values18.4 %
A028883Primes of the form k^2 - 7primes100.0 %
A028884a(n) = (n + 3)^2 - 8polynomial100.0 %
A028885Numbers k such that k^2 - 8 is primeprime values29.8 %
A028886Primes of the form k^2 - 8primes100.0 %
A028982Squares and twice squaresquadratic form66.5 %
A028983Numbers whose sum of divisors is evendivisor functions9.6 %
A029581Numbers in which all digits are compositedigit rule13.7 %
A029730Numbers that are palindromic in base 16digit rule76.2 %
A029739Numbers that are congruent to {1, 3, 4} mod 6residue class18.0 %
A029742Nonpalindromic numbersdigit rule9.6 %
A029803Numbers that are palindromic in base 8digit rule84.9 %
A029952Palindromic in base 5digit rule78.4 %
A029953Palindromic in base 6digit rule83.2 %
A029954Palindromic in base 7digit rule77.1 %
A029955Palindromic in base 9digit rule79.6 %
A029956Numbers that are palindromic in base 11digit rule75.4 %
A029957Numbers that are palindromic in base 12digit rule79.5 %
A029958Numbers that are palindromic in base 13digit rule80.8 %
A029959Numbers that are palindromic in base 14digit rule83.4 %
A029960Numbers that are palindromic in base 15digit rule80.0 %
A030059Numbers that are the product of an odd number of distinct primesmultiplicative14.6 %
A030079Primes p such that digits of p appear in p^2primes33.4 %
A030096Primes whose digits are all oddprimes28.3 %
A030124Complement (and also first differences) of Hofstadter's sequence A005228self-referential9.6 %
A030141Numbers in which parity of the decimal digits alternatesdigit rule14.3 %
A030143Even numbers in which parity of digits alternatesdigit rule9.6 %
A030144Primes in which parity of digits alternatesprimes27.8 %
A030229Numbers that are the product of an even number of distinct primesmultiplicative14.7 %
A030230Numbers that have an odd number of distinct prime divisorsmultiplicative12.7 %
A030231Numbers with an even number of distinct prime factorsmultiplicative12.7 %
A030430Primes of the form 10*n+1primes37.2 %
A030431Primes of form 10n+3primes37.3 %
A030432Primes of form 10n+7primes37.3 %
A030433Primes of form 10*k + 9primes37.3 %
A030457Numbers k such that k concatenated with k+1 is primedigit rule26.2 %
A030459Prime p concatenated with next prime is also primeprimes45.6 %
A030513Numbers with 4 divisorsdivisor functions15.7 %
A030515Numbers with exactly 6 divisorsdivisor functions27.4 %
A030626Numbers with exactly 8 divisorsdivisor functions16.5 %
A0306281 together with numbers of the form p*q^4 and p^9, where p and q are distinct primesdivisor functions29.8 %
A030630Numbers with 12 divisorsdivisor functions21.3 %
A030632Numbers with 14 divisorsmultiplicative28.9 %
A030634Numbers with 16 divisorsdivisor functions19.9 %
A030636Numbers with 18 divisorsmultiplicative33.9 %
A030638Numbers with 20 divisorsdivisor functions25.9 %
A031177Unhappy numbers: numbers having period-8 2-digitized sequencesdigit rule10.4 %
A031363Positive numbers of the form x^2 + xy - y^2; or, of the form 5x^2 - y^2multiplicative23.4 %
A031368Odd-indexed primes: a(n) = prime(2n-1)primes31.1 %
A031443Digitally balanced numbers: positive numbers that in base 2 have the same number of 0's as 1'sbinary rule11.8 %
A031879Nonprime lucky numberssieve32.0 %
A031924Primes followed by a gap of 6, i.e., next prime is p + 6primes36.0 %
A031925Upper prime of a difference of 6 between consecutive primesprimes46.9 %
A031926Lower prime of a difference of 8 between consecutive primesprimes49.2 %
A031928Lower prime of a difference of 10 between consecutive primesprimes47.7 %
A031930Lower prime of a difference of 12 between consecutive primesprimes40.5 %
A031932Lower prime of a pair of consecutive primes having a difference of 14primes50.8 %
A031934Lower prime of a pair of consecutive primes having a difference of 16primes52.3 %
A031936Lower prime of a difference of 18 between consecutive primesprimes43.1 %
A031938Lower prime of a difference of 20 between consecutive primesprimes53.0 %
A031955Numbers with exactly two distinct base-10 digitsdigit rule22.9 %
A032352Numbers k such that there is no prime between 10*k and 10*k+9primes14.4 %
A032766Numbers that are congruent to 0 or 1 (mod 3)residue class17.6 %
A032769Numbers that are congruent to {0, 1, 2, 4} mod 5residue class5.9 %
A032775Numbers that are congruent to {0, 1, 2, 3, 5, 6} mod 7residue class10.2 %
A032793Numbers that are congruent to {1, 2, 4} mod 5residue class5.8 %
A032796Numbers that are congruent to {1, 2, 3, 5, 6} mod 7residue class11.0 %
A032810Numbers using only digits 2 and 3digit rule12.4 %
A032822Numbers whose set of base-10 digits is {1,4}digit rule14.7 %
A032834Numbers with digits 3 and 4 onlydigit rule6.3 %
A032917Numbers having only digits 1 and 3 in their decimal representationdigit rule14.0 %
A032924Numbers whose ternary expansion contains no 0digit rule4.9 %
A032981Positive numbers with the property that all pairs of consecutive base-10 digits differ by 0 or 1digit rule11.7 %
A033015Numbers whose base-2 expansion has no run of digits with length < 2binary rule19.1 %
A033199Primes of form x^2+6*y^2quadratic form39.5 %
A033200Primes congruent to {1, 3} (mod 8); or, odd primes of form x^2 + 2*y^2primes28.5 %
A033201Primes of the form x^2 + 10*y^2quadratic form37.0 %
A033202Primes of form x^2+93*y^2quadratic form44.0 %
A033204Primes of form x^2 + 94*y^2quadratic form42.5 %
A033205Primes of form x^2 + 5*y^2primes36.7 %
A033206Primes of form x^2+95*y^2quadratic form47.5 %
A033208Primes of form x^2+97*y^2quadratic form38.0 %
A033209Primes of form x^2 + 11*y^2quadratic form37.9 %
A033210Primes of the form x^2+13*y^2quadratic form35.2 %
A033211Primes of form x^2 + 14*y^2quadratic form35.9 %
A033212Primes congruent to 1 or 19 (mod 30)primes43.8 %
A033213Primes of form x^2+17*y^2quadratic form37.0 %
A033214Primes of form x^2+19*y^2quadratic form37.9 %
A033215Primes of form x^2+21*y^2quadratic form41.7 %
A033216Primes of form x^2+22*y^2quadratic form35.3 %
A033217Primes of form x^2 + 23*y^2quadratic form35.3 %
A033218Primes of form x^2+26*y^2quadratic form42.5 %
A033219Primes of form x^2+29*y^2quadratic form41.7 %
A033220Primes of form x^2+30*y^2quadratic form48.2 %
A033221Primes of form x^2+31*y^2quadratic form35.6 %
A033222Primes of form x^2+33*y^2quadratic form46.3 %
A033223Primes of form x^2+34*y^2quadratic form37.4 %
A033224Primes of form x^2+35*y^2quadratic form42.1 %
A033225Primes of form x^2+37*y^2quadratic form34.2 %
A033226Primes of form x^2+38*y^2quadratic form42.5 %
A033227Primes of form x^2+39*y^2quadratic form45.2 %
A033228Primes of form x^2+41*y^2quadratic form42.5 %
A033229Primes of form x^2+42*y^2quadratic form42.1 %
A033230Primes of form x^2+43*y^2quadratic form37.3 %
A033231Primes of form x^2+46*y^2quadratic form36.9 %
A033232Primes of form x^2+47*y^2quadratic form39.5 %
A033233Primes of form x^2+51*y^2quadratic form45.4 %
A033234Primes of form x^2+53*y^2quadratic form41.5 %
A033235Primes of the form x^2 + 55*y^2quadratic form43.1 %
A033236Primes of form x^2+57*y^2quadratic form45.5 %
A033237Primes of form x^2+58*y^2quadratic form34.5 %
A033238Primes of form x^2+59*y^2quadratic form44.5 %
A033239Primes of form x^2+61*y^2quadratic form41.6 %
A033240Primes of form x^2+62*y^2quadratic form42.4 %
A033241Primes of form x^2+65*y^2quadratic form47.9 %
A033242Primes of form x^2+66*y^2quadratic form50.2 %
A033243Primes of form x^2+67*y^2quadratic form37.0 %
A033244Primes of form x^2+69*y^2quadratic form47.3 %
A033245Primes of form x^2+70*y^2quadratic form39.1 %
A033246Primes of form x^2+71*y^2quadratic form41.7 %
A033247Primes of form x^2+73*y^2quadratic form37.8 %
A033248Primes of the form x^2+74*y^2quadratic form45.3 %
A033249Primes of form x^2+77*y^2quadratic form42.3 %
A033250Primes of form x^2+78*y^2quadratic form45.5 %
A033251Primes of form x^2+79*y^2quadratic form39.5 %
A033252Primes of form x^2+82*y^2quadratic form37.8 %
A033253Primes of form x^2+83*y^2quadratic form44.1 %
A033254Primes of form x^2+85*y^2quadratic form40.5 %
A033255Primes of form x^2+86*y^2quadratic form45.3 %
A033256Primes of form x^2+87*y^2quadratic form47.4 %
A033257Primes of form x^2+89*y^2quadratic form45.6 %
A033258Primes of form x^2+91*y^2quadratic form40.3 %
A033286a(n) = n * prime(n)primes100.0 %
A033298a(n+1) = a(n) + sum of digits of a(n)^2, with a(1) = 1digit rule32.1 %
A033428a(n) = 3*n^2polynomial100.0 %
A033429a(n) = 5*n^2polynomial100.0 %
A033430a(n) = 4*n^3polynomial100.0 %
A033431a(n) = 2*n^3polynomial100.0 %
A033537a(n) = n*(2*n+5)polynomial100.0 %
A033556a(n+1) = 2a(n) - {largest prime < a(n)}primes100.0 %
A033560Primes p such that 4!+p is also primeprimes35.2 %
A033562a(n) = 2*n^3 + 1polynomial100.0 %
A033567a(n) = (2*n-1)*(4*n-1)polynomial100.0 %
A033568Second pentagonal numbers with odd index: a(n) = (2*n-1)*(3*n-1)polynomial100.0 %
A033571a(n) = (2*n + 1)*(5*n + 1)polynomial100.0 %
A033572a(n) = (2*n+1)*(7*n+1)polynomial100.0 %
A033573a(n) = (2*n+1)*(9*n+1)polynomial100.0 %
A033574a(n) = (2*n+1)*(10*n+1)polynomial100.0 %
A033575a(n) = (2*n+1)*(11*n+1)polynomial100.0 %
A033576a(n) = (2*n+1)*(12*n+1)polynomial100.0 %
A033577a(n) = (3*n+1)*(4*n+1)polynomial100.0 %
A033578a(n) = (3*n - 1)*(4*n - 1)polynomial100.0 %
A033581a(n) = 6*n^2polynomial100.0 %
A033582a(n) = 7*n^2polynomial100.0 %
A033583a(n) = 10*n^2polynomial100.0 %
A033584a(n) = 11*n^2polynomial100.0 %
A033585a(n) = 2*n*(4*n + 1)polynomial100.0 %
A033586a(n) = 4*n*(2*n + 1)polynomial100.0 %
A033587a(n) = 2*n*(4*n + 3)polynomial100.0 %
A033816a(n) = 2*n^2 + 3*n + 3polynomial100.0 %
A033868Numbers n such that 7*n-11 is primeprime values21.3 %
A033948Numbers that have a primitive root (k such that the multiplicative group modulo k is cyclic)multiplicative15.3 %
A033949Positive integers that do not have a primitive rootmultiplicative11.6 %
A033950Refactorable numbers: number of divisors of k divides k. Also known as tau numbersmultiplicative16.9 %
A033991a(n) = n*(4*n-1)polynomial100.0 %
A033992Numbers that are divisible by exactly three different primesmultiplicative13.6 %
A033993Numbers that are divisible by exactly four different primesmultiplicative17.2 %
A033994a(n) = n*(n+1)*(5*n+1)/6polynomial100.0 %
A034017Numbers that are primitively represented by x^2 + xy + y^2quadratic form29.7 %
A034020Not of the form x^2 + x*y + y^2quadratic form9.2 %
A034048Numbers with multiplicative digital root value 0digit rule10.2 %
A034262a(n) = n^3 + npolynomial100.0 %
A034470Prime numbers using only the curved digits 0, 2, 3, 5, 6, 8 and 9primes29.9 %
A034683Unitary abundant numbers: numbers k such that usigma(k) > 2*kdivisor functions14.6 %
A034705Numbers that are sums of consecutive squaressummatory38.5 %
A034707Numbers that are sums (of a nonempty sequence) of consecutive primesprimes13.1 %
A034709Numbers divisible by their last digitdigit rule15.2 %
A034721a(n) = (10*n^3 - 9*n^2 + 2*n)/3 + 1polynomial100.0 %
A034837Numbers that are divisible by the first, i.e., the leftmost, digitdigit rule9.2 %
A034838Numbers k that are divisible by every digit of kdigit rule14.7 %
A034844Primes with only nonprime decimal digitsprimes34.6 %
A034936Numbers k such that 3*k + 4 is primeprime values26.6 %
A034961Sums of three consecutive primesprimes41.7 %
A034962Primes that are the sum of three consecutive primesprimes45.0 %
A034963Sums of four consecutive primesprimes31.4 %
A034965Primes that are sum of five consecutive primesprimes49.7 %
A035005Number of possible queen moves on an n X n chessboardpolynomial100.0 %
A035006Number of possible rook moves on an n X n chessboardpolynomial100.0 %
A035008Total number of possible knight moves on an (n+2) X (n+2) chessboard, if the knight is placed anywherepolynomial100.0 %
A0351061, together with numbers of the form k*(k+1) or k*(k+2), k > 0polynomial100.0 %
A035121Numbers of the form x^2+82*y^2quadratic form20.5 %
A035328a(n) = n*(2*n-1)*(2*n+1)polynomial100.0 %
A035329a(n) = n*(2*n+5)*(2*n+7)polynomial100.0 %
A035333Concatenation of two or more consecutive positive integersdigit rule99.9 %
A035336a(n) = 2*floor(n*phi) + n - 1, where phi = (1+sqrt(5))/2Beatty18.6 %
A035497Happy primes: primes that eventually reach 1 under iteration of "x -> sum of squares of digits of x"primes37.8 %
A035928Numbers n such that BCR(n) = n, where BCR = binary-complement-and-reverse = take one's complement then reverse bit orderbinary rule84.4 %
A036301Numbers whose sum of even digits and sum of odd digits are equaldigit rule28.8 %
A036433Number of divisors is a digit in the base 10 representation of ndivisor functions12.9 %
A036435Digits are nonzero squaresdigit rule18.1 %
A036441a(n+1) = next number having largest prime dividing a(n) as a factor, with a(1) = 2self-referential100.0 %
A036455Numbers n such that d(d(n)) is an odd prime, where d(k) is the number of divisors of kdivisor functions14.2 %
A036537Numbers whose number of divisors is a power of 2divisor functions10.2 %
A036554Numbers whose binary representation ends in an odd number of zerosbinary rule13.9 %
A036668Hati numbers: of form 2^i*3^j*k, i+j even, (k,6)=1multiplicative13.1 %
A036689Product of a prime and the previous numberprimes100.0 %
A036690Product of a prime and the following numberprimes100.0 %
A036785Numbers divisible by the squares of two distinct primesmultiplicative19.2 %
A036953Primes having only {0, 1, 2} as digitsprimes36.5 %
A036956Primes containing only digits from the set (0,1,2,3,4)primes28.8 %
A036958Primes containing only digits from the set (0,1,2,3,4,5)primes28.6 %
A036960Primes containing only digits from the set (0,1,2,3,4,5,6)primes28.1 %
A036962Primes without {8, 9} as digitsprimes26.9 %
A036990Numbers n such that, in the binary expansion of n, reading from right to left, the number of 1's never exceeds the number of 0'sbinary rule4.7 %
A037020Numbers whose sum of proper (or aliquot) divisors is a primemultiplicative28.4 %
A037029Primes of the form 666*n + 1primes69.1 %
A037030Numbers n such that 666*n + 1 is primeprime values19.5 %
A037085Beatty sequence for Pi^2Beatty24.8 %
A037086Beatty sequence for sqrt(Pi)Beatty12.8 %
A037087Beatty sequence for e^(1/e)Beatty11.4 %
A037123a(n) = a(n-1) + sum of digits of nsummatory28.3 %
A037144Numbers with at most 3 prime factors (counted with multiplicity)multiplicative9.6 %
A037235a(n) = n*(2*n^2 - 3*n + 4)/3polynomial100.0 %
A037301Numbers whose base-2 and base-3 expansions have the same digit sumdigit rule17.9 %
A037308Numbers whose base-2 and base-10 expansions have the same digit sumdigit rule21.3 %
A037372Positive numbers k such that every base-2 digit of k is a base-3 digit of kdigit rule9.5 %
A037373Positive numbers k such that every base-2 digit of k is a base-4 digit of kdigit rule9.7 %
A037374Positive numbers k such that every base-2 digit of k is a base-5 digit of kdigit rule10.0 %
A037380Numbers whose base-3 digits are all present among their base-4 digitsdigit rule9.7 %
A037386Every base 3 digit of n is a base 10 digit of ndigit rule14.1 %
A038130Beatty sequence for 2*PiBeatty21.9 %
A038152Beatty sequence for e^PiBeatty30.7 %
A038153Beatty sequence for Pi^eBeatty30.5 %
A038366n is divisible by (product of digits) + (sum of digits)digit rule19.4 %
A038367Numbers n with property that (product of digits of n) is divisible by (sum of digits of n)digit rule11.8 %
A038368n is divisible by |(product of digits) - (sum of digits)|digit rule19.5 %
A038509Composite numbers congruent to +-1 mod 6multiplicative15.1 %
A038550Products of an odd prime and a power of two (sorted)primes12.0 %
A038580Primes with indices that are primes with prime indicesprimes64.6 %
A038599Numbers k such that k^3 - 2 is primeprime values35.4 %
A038603Primes not containing the digit '1'primes25.0 %
A038604Primes not containing the digit '2'primes23.5 %
A038611Primes not containing the digit '3'primes27.4 %
A038612Primes not containing the digit '4'primes23.8 %
A038613Primes not containing the digit '5'primes23.6 %
A038614Primes not containing the digit '6'primes23.6 %
A038615Primes not containing the digit '7'primes25.3 %
A038617Primes not containing the digit '9'primes26.8 %
A038618Primes not containing the digit '0'primes23.6 %
A038764a(n) = (9*n^2 + 3*n + 2)/2polynomial100.0 %
A038770Numbers divisible by at least one of their digitsdigit rule11.1 %
A038772Numbers not divisible by any of their digitsdigit rule10.9 %
A038812Number of primes less than 1000nprimes36.7 %
A038865a(n) = (n+3)^3 - n^3polynomial100.0 %
A038866a(n) = (n+4)^3 - n^3polynomial100.0 %
A038867a(n) = (n+5)^3 - n^3polynomial100.0 %
A038873Primes p such that 2 is a square mod p; or, primes congruent to {1, 2, 7} mod 8primes28.3 %
A039004Numbers whose base-4 representation has the same number of 1's and 2'sdigit rule10.8 %
A039770Numbers k such that phi(k) is a perfect squaredivisor functions41.3 %
A039787Primes p such that p-1 is squarefreeprimes30.0 %
A039949Primes of the form 30n - 13primes48.5 %
A039955Squarefree numbers congruent to 1 (mod 4)multiplicative22.9 %
A039956Even squarefree numbersmultiplicative17.5 %
A039957Squarefree numbers congruent to 3 mod 4multiplicative23.0 %
A040098Primes p such that x^4 = 2 has a solution mod pprimes30.5 %
A040117Primes congruent to 5 (mod 12). Also primes p such that x^4 = 9 has no solution mod pprimes40.3 %
A040976a(n) = prime(n) - 2primes30.6 %
A042963Numbers congruent to 1 or 2 mod 4residue class12.3 %
A042965Nonnegative integers not congruent to 2 mod 4residue class12.5 %
A042987Primes congruent to {2, 3, 5, 7} mod 8primes25.1 %
A042988Primes not congruent to -1 (mod 7)primes25.7 %
A042989Primes congruent to {0, 2, 3, 4, 5} mod 7primes27.3 %
A042990Primes not congruent to 4 (mod 7)primes24.3 %
A042992Primes congruent to {0, 2, 3, 5, 6} (mod 7)primes24.8 %
A042994Primes congruent to {0, 1, 2, 3, 5} (mod 7)primes27.7 %
A042995Primes congruent to {0, 2, 3, 5} (mod 7)primes29.5 %
A042997Primes congruent to {2, 3, 4, 5, 6} (mod 7)primes24.1 %
A042998Primes congruent to {1, 2, 3, 5} (mod 8)primes25.0 %
A043096Numbers in which every pair of adjacent digits are distinctdigit rule9.7 %
A043489Numbers having one 0 in base 10digit rule9.9 %
A043493Numbers that contain a single 1digit rule11.3 %
A044102Multiples of 36residue class9.6 %
A045315Primes p such that x^8 = 2 has a solution mod pprimes31.7 %
A045320Primes not congruent to 5 (mod 7)primes25.0 %
A045321Primes congruent to {1, 2, 3} (mod 5)primes26.1 %
A045322Primes congruent to {0, 2, 3, 4, 6} (mod 7)primes26.9 %
A045323Primes congruent to {1, 2, 3, 7} (mod 8)primes25.3 %
A045324Primes congruent to {0, 1, 2, 3, 4} (mod 7)primes26.4 %
A045325Primes congruent to {0, 2, 3, 4} (mod 7)primes28.9 %
A045327Primes congruent to {2, 3, 4} mod 5primes25.0 %
A045328Primes congruent to {0, 1, 2, 3, 6} (mod 7)primes27.4 %
A045329Primes congruent to {0, 2, 3, 6} (mod 7)primes29.4 %
A045342Primes congruent to {1, 2, 3} mod 7primes29.6 %
A045343Primes congruent to {2, 3} mod 7primes33.8 %
A045346Primes congruent to {0, 1, 2, 4, 5, 6} mod 7primes24.4 %
A045347Primes congruent to {0, 2, 4, 5, 6} mod 7primes26.0 %
A045350Primes congruent to {0, 1, 2, 4, 5} mod 7primes26.6 %
A045351Primes congruent to {0, 2, 4, 5} mod 7primes29.4 %
A045352Primes congruent to {1, 2, 5, 7} mod 8primes25.0 %
A045353Primes congruent to {0, 1, 2, 5, 6} mod 7primes26.4 %
A045354Primes congruent to {0, 2, 5, 6} mod 7primes27.8 %
A045358Primes congruent to {0, 1, 2, 5} mod 7primes30.1 %
A045368Primes congruent to {2, 5} mod 7primes34.3 %
A045369Primes congruent to {0, 1, 2, 4, 6} mod 7primes26.3 %
A045370Primes congruent to {0, 2, 4, 6} mod 7primes29.4 %
A045371Primes congruent to {1, 2, 4} mod 5primes26.6 %
A045372Primes congruent to {1, 2} mod 5primes30.3 %
A045376Primes congruent to {0, 1, 2, 6} mod 7primes29.6 %
A045378Primes congruent to {2, 4} mod 5primes29.0 %
A045386Primes congruent to {1, 2, 4} mod 7primes25.9 %
A045387Primes congruent to {2, 4} mod 7primes29.5 %
A045389Primes congruent to {2, 6} mod 7primes34.4 %
A045391Primes congruent to {1, 2} mod 7primes30.0 %
A045392Primes congruent to 2 mod 7primes39.1 %
A045393Primes congruent to {0, 1, 3, 4, 5, 6} mod 7primes23.7 %
A045394Primes congruent to {0, 3, 4, 5, 6} mod 7primes24.8 %
A045396Primes congruent to {0, 1, 3, 4, 5} mod 7primes27.5 %
A045397Primes congruent to {0, 3, 4, 5} mod 7primes29.8 %
A045398Primes congruent to {0, 1, 3, 5, 6} mod 7primes24.7 %
A045400Primes congruent to {0, 1, 3, 5} mod 7primes29.6 %
A045416Primes congruent to {3, 5} mod 7primes29.9 %
A045417Primes congruent to {0, 1, 3, 4, 6} mod 7primes26.3 %
A045418Primes congruent to {0, 3, 4, 6} mod 7primes28.7 %
A045420Primes congruent to {0, 1, 3, 4} mod 7primes29.2 %
A045422Primes congruent to {0, 1, 3, 6} mod 7primes28.7 %
A045428Primes congruent to {1, 3, 4} mod 5primes24.4 %
A045429Primes congruent to {1, 3} mod 5primes27.1 %
A045432Primes congruent to {3, 4} mod 7primes34.0 %
A045434Primes congruent to {3, 6} mod 7primes29.0 %
A045435Primes congruent to {3, 4} mod 5primes26.0 %
A045436Primes congruent to {1, 3} mod 7primes33.9 %
A045437Primes congruent to 3 mod 7primes38.7 %
A045438Primes congruent to {0, 1, 4, 5, 6} mod 7primes26.3 %
A045439Primes congruent to {0, 4, 5, 6} mod 7primes27.7 %
A045440Primes congruent to {0, 1, 4, 5} mod 7primes29.6 %
A045443Primes congruent to {0, 1, 5, 6} mod 7primes28.1 %
A045452Primes congruent to {4, 5} mod 7primes34.0 %
A045455Primes congruent to {5, 6} mod 7primes27.5 %
A045456Primes congruent to {1, 5} mod 7primes34.6 %
A045458Primes congruent to 5 mod 7primes39.0 %
A045459Primes congruent to {0, 1, 4, 6} mod 7primes29.5 %
A045465Primes congruent to {0, 1} mod 7primes38.9 %
A045467Primes congruent to {4, 6} mod 7primes34.1 %
A045468Primes congruent to {1, 4} mod 5primes31.8 %
A045469Primes congruent to {1, 4} mod 7primes30.0 %
A045471Primes congruent to 4 mod 7primes39.1 %
A045472Primes congruent to {1, 6} mod 7primes33.7 %
A045473Primes congruent to 6 mod 7primes39.1 %
A045542Sub-perfect powers: perfect powers (squares, cubes etc., not including 1) minus 1powers99.3 %
A045546Numbers k such that k^2 + k - 1 is primeprime values20.2 %
A045572Numbers that are odd but not divisible by 5residue class18.6 %
A045636Numbers of the form p^2 + q^2, with p and q primesprimes44.4 %
A045699Numbers of the form p^2 + q^3, p,q primeprimes48.6 %
A045707Primes with first digit 1primes21.4 %
A045708Primes with first digit 2primes21.1 %
A045746Numbers whose sum of divisors is a triangular numberdivisor functions63.0 %
A045753Numbers n such that 4n-1 and 4n+1 are both primesprime values31.9 %
A045776a(n+1) is smallest multiple of (sum of digits of a(n)) which is > a(n)self-referential10.8 %
A045797Evenish numbers (prime to 10 and 10's digit is even)residue class21.6 %
A045798Oddish numbers (prime to 10 and 10's digit is odd)residue class21.5 %
A045844a(n+1) = a(n) + largest digit of a(n); a(0) = 1self-referential16.9 %
A045920Numbers m such that the factorizations of m..m+1 have the same number of primes (including multiplicities)multiplicative20.1 %
A045926All digits even and nonzerodigit rule11.2 %
A045939Numbers m such that the factorizations of m..m+2 have the same number of primes (including multiplicities)multiplicative30.4 %
A045943Triangular matchstick numbers: a(n) = 3*n*(n+1)/2polynomial100.0 %
A045944Rhombic matchstick numbers: a(n) = n*(3*n+2)polynomial100.0 %
A045946Star of David matchstick numbers: a(n) = 6*n*(3*n+1)polynomial100.0 %
A045954Even-Lucky-Numbers: generated by a sieve process like that for Lucky numbers but starting with even numberssieve20.6 %
A045980Numbers of the form x^3 + y^3 or x^3 - y^3quadratic form40.2 %
A046025Numbers k such that 6*k+1, 12*k+1 and 18*k+1 are all primesprime values44.7 %
A046030Numbers whose digits are squaresdigit rule15.6 %
A046031Digits are cubesdigit rule15.8 %
A046034Numbers whose digits are primesdigit rule17.3 %
A046099Numbers that are not cubefree. Numbers divisible by a cube greater than 1. Complement of A004709multiplicative14.1 %
A046100Biquadratefree numbers: numbers that are not divisible by any 4th power greater than 1multiplicative9.9 %
A046101Biquadrateful numbersmultiplicative13.7 %
A046133Primes p such that p + 12 is also primeprimes35.2 %
A046134p, p+2 and p+8 are primesprimes65.9 %
A046135Primes p such that p+2 and p+12 are primesprimes59.7 %
A046136Primes p such that p, p+4 and p+10 are primesprimes60.2 %
A046137Primes p such that p+4 and p+12 are also primeprimes63.4 %
A046138Primes p such that p+6 and p+8 are also primesprimes63.7 %
A046139p, p+6 and p+10 are primesprimes58.9 %
A046141p, p+8 and p+12 are primesprimes66.3 %
A046306Numbers that are divisible by exactly 6 primes with multiplicitymultiplicative19.0 %
A046308Numbers that are divisible by exactly 7 primes counting multiplicitymultiplicative19.7 %
A046310Numbers that are divisible by exactly 8 primes counting multiplicitymultiplicative20.5 %
A046312Numbers that are divisible by exactly 9 primes with multiplicitymultiplicative21.2 %
A046314Numbers that are divisible by exactly 10 primes with multiplicitymultiplicative21.9 %
A046315Odd semiprimes: odd numbers divisible by exactly 2 primes (counted with multiplicity)multiplicative21.0 %
A046316Numbers of the form p*q*r where p,q,r are (not necessarily distinct) odd primesmultiplicative25.7 %
A046386Products of exactly four distinct primesmultiplicative21.0 %
A046387Products of exactly 5 distinct primesmultiplicative25.6 %
A046388Odd numbers of the form p*q where p and q are distinct primesmultiplicative21.0 %
A046642Numbers k such that k and number of divisors d(k) are relatively primedivisor functions16.7 %
A046704Additive primes: sum of digits is a primeprimes31.1 %
A046711From the Bruck-Ryser theorem: numbers n == 1 or 2 (mod 4) which are also the sum of 2 squaresquadratic form17.9 %
A046712From the Bruck-Ryser theorem: n == 1 or 2 (mod 4) which are not the sum of 2 squaresquadratic form15.3 %
A046758Equidigital numbersdigit rule16.2 %
A046759Economical numbers: write n as a product of primes raised to powers, let D(n) = number of digits in product, l(n) = number of digits in n; sequence gives n such that D(n) < l(n)digit rule41.2 %
A046760Wasteful numbersdigit rule11.5 %
A046869Good primes (version 1): prime(n)^2 > prime(n-1)*prime(n+1)primes30.9 %
A046953Numbers k such that 6*k - 1 is compositecomplement10.3 %
A046992a(n) = Sum_{k=1..n} pi(k) (cf. A000720)summatory70.3 %
A047078Primes at which difference pattern X2Y (X and Y >= 6) occurs in A001223primes49.8 %
A047201Numbers not divisible by 5forced divisor10.4 %
A047202Numbers that are congruent to {2, 3, 4} mod 5residue class14.9 %
A047203Numbers that are congruent to {0, 2, 3, 4} mod 5residue class13.3 %
A047204Numbers that are congruent to {3, 4} mod 5residue class5.5 %
A047205Numbers that are congruent to {0, 3, 4} mod 5residue class14.9 %
A047206Numbers that are congruent to {1, 3, 4} mod 5residue class15.5 %
A047207Numbers that are congruent to {0, 1, 3, 4} mod 5residue class13.3 %
A047208Numbers that are congruent to {0, 4} mod 5residue class17.6 %
A047209Numbers that are congruent to {1, 4} mod 5residue class18.9 %
A047211Numbers that are congruent to {2, 4} mod 5residue class10.5 %
A047212Numbers that are congruent to {0, 2, 4} mod 5residue class9.7 %
A047215Numbers that are congruent to {0, 2} mod 5residue class18.9 %
A047216Numbers that are congruent to {1, 2} mod 5residue class12.0 %
A047217Numbers that are congruent to {0, 1, 2} mod 5residue class11.1 %
A047218Numbers that are congruent to {0, 3} mod 5residue class18.9 %
A047219Numbers that are congruent to {1, 3} mod 5residue class8.5 %
A047220Numbers that are congruent to {0, 1, 3} mod 5residue class15.5 %
A047221Numbers that are congruent to {2, 3} mod 5residue class17.5 %
A047222Numbers that are congruent to {0, 2, 3} mod 5residue class15.5 %
A047223Numbers that are congruent to {1, 2, 3} mod 5residue class3.8 %
A047225Numbers that are congruent to {0, 1} mod 6residue class23.6 %
A047227Numbers that are congruent to {1, 2, 3, 4} mod 6residue class13.8 %
A047228Numbers that are congruent to {2, 3, 4} mod 6residue class9.0 %
A047229Numbers that are congruent to {0, 2, 3, 4} mod 6residue class14.3 %
A047230Numbers that are congruent to {3, 4} mod 6residue class16.0 %
A047231Numbers that are congruent to {0, 3, 4} mod 6residue class11.4 %
A047233Numbers that are congruent to {0, 4} mod 6residue class17.5 %
A047234Numbers that are congruent to {0, 1, 4} mod 6residue class18.6 %
A047235Numbers that are congruent to {2, 4} mod 6residue class0.0 %
A047236Numbers that are congruent to {1, 2, 4} mod 6residue class9.0 %
A047237Numbers that are congruent to {0, 1, 2, 4} mod 6residue class10.6 %
A047238Numbers that are congruent to {0, 2} mod 6residue class17.6 %
A047240Numbers that are congruent to {0, 1, 2} mod 6residue class16.4 %
A047241Numbers that are congruent to {1, 3} mod 6residue class26.1 %
A047242Numbers that are congruent to {0, 1, 3} mod 6residue class18.0 %
A047243Numbers that are congruent to {2, 3} mod 6residue class23.6 %
A047244Numbers that are congruent to {0, 2, 3} mod 6residue class13.8 %
A047245Numbers that are congruent to {1, 2, 3} mod 6residue class18.0 %
A047246Numbers that are congruent to {0, 1, 2, 3} mod 6residue class13.8 %
A047249Numbers that are congruent to {3, 4, 5} mod 6residue class9.0 %
A047252Numbers that are congruent to {0, 1, 3, 4, 5} mod 6residue class11.3 %
A047253Numbers that are congruent to {1, 2, 3, 4, 5} mod 6residue class5.6 %
A047254Numbers that are congruent to {2, 3, 5} mod 6residue class22.8 %
A047255Numbers that are congruent to {1, 2, 3, 5} mod 6residue class13.8 %
A047256Numbers that are congruent to {0, 1, 2, 3, 5} mod 6residue class16.9 %
A047257Numbers that are congruent to {4, 5} mod 6residue class0.0 %
A047258Numbers that are congruent to {0, 4, 5} mod 6residue class7.4 %
A047259Numbers that are congruent to {1, 4, 5} mod 6residue class4.8 %
A047260Numbers that are congruent to {0, 1, 4, 5} mod 6residue class10.7 %
A047261Numbers that are congruent to {2, 4, 5} mod 6residue class4.8 %
A047262Numbers that are congruent to {0, 2, 4, 5} mod 6residue class3.7 %
A047263Numbers that are congruent to {0, 1, 2, 4, 5} mod 6residue class5.7 %
A047266Numbers that are congruent to {0, 1, 5} mod 6residue class15.6 %
A047267Numbers that are congruent to {0, 2, 5} mod 6residue class13.8 %
A047268Numbers that are congruent to {1, 2, 5} mod 6residue class9.0 %
A047269Numbers that are congruent to {0, 1, 2, 5} mod 6residue class13.9 %
A047270Numbers that are congruent to {3, 5} mod 6residue class25.9 %
A047271Numbers that are congruent to {0, 3, 5} mod 6residue class15.6 %
A047273Numbers that are congruent to {0, 1, 3, 5} mod 6residue class20.8 %
A047274Numbers that are congruent to {0, 1} mod 7residue class18.0 %
A047275Numbers that are congruent to {0, 1, 6} mod 7residue class15.3 %
A047276Numbers that are congruent to {2, 6} mod 7residue class20.4 %
A047277Numbers that are congruent to {0, 2, 6} mod 7residue class16.3 %
A047278Numbers that are congruent to {1, 2, 6} mod 7residue class12.8 %
A047279Numbers that are congruent to {0, 1, 2, 6} mod 7residue class11.1 %
A047280Numbers that are congruent to {3, 6} mod 7residue class10.9 %
A047281Numbers that are congruent to {0, 3, 6} mod 7residue class10.0 %
A047282Numbers that are congruent to {1, 3, 6} mod 7residue class10.6 %
A047283Numbers that are congruent to {0, 1, 3, 6} mod 7residue class9.4 %
A047284Numbers that are congruent to {2, 3, 6} mod 7residue class10.0 %
A047285Numbers that are congruent to {0, 2, 3, 6} mod 7residue class9.4 %
A047286Numbers that are congruent to {1, 2, 3, 6} mod 7residue class6.7 %
A047287Numbers that are congruent to {0, 1, 2, 3, 6} mod 7residue class6.5 %
A047288Numbers that are congruent to {4, 6} mod 7residue class19.7 %
A047289Numbers that are congruent to {0, 4, 6} mod 7residue class16.3 %
A047290Numbers that are congruent to {1, 4, 6} mod 7residue class17.1 %
A047291Numbers that are congruent to {0, 1, 4, 6} mod 7residue class14.4 %
A047292Numbers that are congruent to {2, 4, 6} mod 7residue class11.8 %
A047293Numbers that are congruent to {0, 2, 4, 6} mod 7residue class10.8 %
A047294Numbers that are congruent to {1, 2, 4, 6} mod 7residue class8.1 %
A047295Numbers that are congruent to {0, 1, 2, 4, 6} mod 7residue class7.7 %
A047296Numbers that are congruent to {3, 4, 6} mod 7residue class16.2 %
A047297Numbers that are congruent to {0, 3, 4, 6} mod 7residue class14.4 %
A047298Numbers that are congruent to {1, 3, 4, 6} mod 7residue class14.8 %
A047299Numbers that are congruent to {0, 1, 3, 4, 6} mod 7residue class13.1 %
A047300Numbers that are congruent to {2, 3, 4, 6} mod 7residue class14.4 %
A047301Numbers that are congruent to {0, 2, 3, 4, 6} mod 7residue class13.2 %
A047302Numbers that are congruent to {1, 2, 3, 4, 6} mod 7residue class11.0 %
A047303Numbers that are congruent to {0, 1, 2, 3, 4, 6} mod 7residue class10.1 %
A047305Numbers that are congruent to {2, 3, 4, 5, 6} mod 7residue class12.8 %
A047306Numbers that are congruent to {0, 2, 3, 4, 5, 6} mod 7residue class12.0 %
A047307Numbers that are congruent to {3, 4, 5, 6} mod 7residue class13.8 %
A047308Numbers that are congruent to {0, 3, 4, 5, 6} mod 7residue class12.8 %
A047309Numbers that are congruent to {1, 3, 4, 5, 6} mod 7residue class13.1 %
A047310Numbers that are congruent to {0, 1, 3, 4, 5, 6} mod 7residue class12.0 %
A047311Numbers that are congruent to {4, 5, 6} mod 7residue class15.3 %
A047312Numbers that are congruent to {0, 4, 5, 6} mod 7residue class13.8 %
A047313Numbers that are congruent to {1, 4, 5, 6} mod 7residue class14.4 %
A047314Numbers that are congruent to {0, 1, 4, 5, 6} mod 7residue class12.8 %
A047315Numbers that are congruent to {2, 4, 5, 6} mod 7residue class10.4 %
A047316Numbers that are congruent to {0, 2, 4, 5, 6} mod 7residue class9.9 %
A047317Numbers that are congruent to {1, 2, 4, 5, 6} mod 7residue class7.6 %
A047318Numbers that are congruent to {0, 1, 2, 4, 5, 6} mod 7residue class7.4 %
A047319Numbers that are congruent to {5, 6} mod 7residue class5.0 %
A047320Numbers that are congruent to {0, 5, 6} mod 7residue class15.3 %
A047321Numbers that are congruent to {1, 5, 6} mod 7residue class16.2 %
A047322Numbers that are congruent to {0, 1, 5, 6} mod 7residue class13.7 %
A047323Numbers that are congruent to {2, 5, 6} mod 7residue class16.6 %
A047324Numbers that are congruent to {0, 2, 5, 6} mod 7residue class14.4 %
A047325Numbers that are congruent to {1, 2, 5, 6} mod 7residue class11.8 %
A047326Numbers that are congruent to {0, 1, 2, 5, 6} mod 7residue class10.6 %
A047327Numbers that are congruent to {3, 5, 6} mod 7residue class16.3 %
A047328Numbers that are congruent to {0, 3, 5, 6} mod 7residue class14.4 %
A047329Numbers that are congruent to {1, 3, 5, 6} mod 7residue class14.8 %
A047330Numbers that are congruent to {0, 1, 3, 5, 6} mod 7residue class13.1 %
A047331Numbers that are congruent to {2, 3, 5, 6} mod 7residue class14.4 %
A047332Numbers that are congruent to {0, 2, 3, 5, 6} mod 7residue class13.2 %
A047335Numbers that are congruent to {0, 6} mod 7residue class18.0 %
A047336Numbers that are congruent to {1, 6} mod 7residue class19.7 %
A047337Numbers that are congruent to {0, 1, 2, 3, 4} mod 7residue class10.6 %
A047338Numbers that are congruent to {1, 2, 3, 4} mod 7residue class5.3 %
A047339Numbers that are congruent to {2, 3, 4} mod 7residue class15.2 %
A047340Numbers that are congruent to {0, 2, 3, 4} mod 7residue class14.4 %
A047341Numbers that are congruent to {3, 4} mod 7residue class18.0 %
A047342Numbers that are congruent to {0, 3, 4} mod 7residue class16.5 %
A047343Numbers that are congruent to {1, 3, 4} mod 7residue class8.7 %
A047344Numbers that are congruent to {0, 1, 3, 4} mod 7residue class14.4 %
A047352Numbers that are congruent to {0, 2} mod 7residue class19.7 %
A047353Numbers that are congruent to {1, 2} mod 7residue class13.1 %
A047393Numbers that are congruent to {0, 1} mod 8residue class20.8 %
A047394Numbers that are congruent to {0, 1, 6} mod 8residue class12.5 %
A047395Numbers that are congruent to {0, 2, 6} mod 8residue class12.5 %
A047396Numbers that are congruent to {1, 2, 6} mod 8residue class14.2 %
A047397Numbers that are congruent to {0, 1, 2, 6} mod 8residue class9.3 %
A047398Numbers that are congruent to {3, 6} mod 8residue class13.5 %
A047399Numbers that are congruent to {0, 3, 6} mod 8residue class8.0 %
A047400Numbers that are congruent to {1, 3, 6} mod 8residue class13.8 %
A047401Numbers that are congruent to {0, 1, 3, 6} mod 8residue class9.0 %
A047402Numbers that are congruent to {2, 3, 6} mod 8residue class12.0 %
A047403Numbers that are congruent to {0, 2, 3, 6} mod 8residue class9.3 %
A047404Numbers that are congruent to {1, 2, 3, 6} mod 8residue class10.6 %
A047405Numbers that are congruent to {0, 1, 2, 3, 6} mod 8residue class7.3 %
A047406Numbers that are congruent to {4, 6} mod 8residue class9.0 %
A047407Numbers that are congruent to {0, 4, 6} mod 8residue class12.8 %
A047408Numbers that are congruent to {1, 4, 6} mod 8residue class20.4 %
A047409Numbers that are congruent to {0, 1, 4, 6} mod 8residue class14.1 %
A047410Numbers that are congruent to {2, 4, 6} mod 8residue class12.4 %
A047411Numbers that are congruent to {1, 2, 4, 6} mod 8residue class10.9 %
A047412Numbers that are congruent to {0, 1, 2, 4, 6} mod 8residue class7.6 %
A047413Numbers that are congruent to {3, 4, 6} mod 8residue class15.5 %
A047414Numbers that are congruent to {0, 3, 4, 6} mod 8residue class11.0 %
A047415Numbers that are congruent to {1, 3, 4, 6} mod 8residue class15.4 %
A047416Numbers that are congruent to {0, 1, 3, 4, 6} mod 8residue class11.3 %
A047417Numbers that are congruent to {2, 3, 4, 6} mod 8residue class14.0 %
A047418Numbers that are congruent to {0, 2, 3, 4, 6} mod 8residue class11.5 %
A047419Numbers that are congruent to {1, 2, 3, 4, 6} mod 8residue class12.6 %
A047420Numbers that are congruent to {0, 1, 2, 3, 4, 6} mod 8residue class9.5 %
A047422Numbers that are congruent to {1, 2, 3, 4, 5, 6} mod 8residue class10.5 %
A047423Numbers that are congruent to {2, 3, 4, 5, 6} mod 8residue class11.2 %
A047424Numbers that are congruent to {0, 2, 3, 4, 5, 6} mod 8residue class9.5 %
A047425Numbers that are congruent to {3, 4, 5, 6} mod 8residue class11.7 %
A047426Numbers that are congruent to {0, 3, 4, 5, 6} mod 8residue class8.7 %
A047427Numbers that are congruent to {1, 3, 4, 5, 6} mod 8residue class12.4 %
A047428Numbers that are congruent to {0, 1, 3, 4, 5, 6} mod 8residue class9.4 %
A047429Numbers that are congruent to {4, 5, 6} mod 8residue class5.9 %
A047430Numbers that are congruent to {0, 4, 5, 6} mod 8residue class9.6 %
A047431Numbers that are congruent to {1, 4, 5, 6} mod 8residue class15.4 %
A047432Numbers that are congruent to {0, 1, 4, 5, 6} mod 8residue class11.3 %
A047433Numbers that are congruent to {2, 4, 5, 6} mod 8residue class9.3 %
A047434Numbers that are congruent to {0, 2, 4, 5, 6} mod 8residue class7.6 %
A047435Numbers that are congruent to {1, 2, 4, 5, 6} mod 8residue class8.7 %
A047436Numbers that are congruent to {5, 6} mod 8residue class15.0 %
A047437Numbers that are congruent to {0, 5, 6} mod 8residue class9.3 %
A047438Numbers that are congruent to {1, 5, 6} mod 8residue class16.0 %
A047439Numbers that are congruent to {0, 1, 5, 6} mod 8residue class10.7 %
A047440Numbers that are congruent to {2, 5, 6} mod 8residue class14.2 %
A047441Numbers that are congruent to {0, 2, 5, 6} mod 8residue class11.0 %
A047442Numbers that are congruent to {0, 1, 2, 5, 6} mod 8residue class8.7 %
A047443Numbers that are congruent to {3, 5, 6} mod 8residue class15.1 %
A047444Numbers that are congruent to {0, 3, 5, 6} mod 8residue class10.6 %
A047445Numbers that are congruent to {1, 3, 5, 6} mod 8residue class15.1 %
A047446Numbers that are congruent to {0, 1, 3, 5, 6} mod 8residue class11.0 %
A047447Numbers that are congruent to {2, 3, 5, 6} mod 8residue class13.7 %
A047448Numbers that are congruent to {0, 2, 3, 5, 6} mod 8residue class11.2 %
A047450Numbers that are congruent to {0, 1, 2, 3, 5, 6} mod 8residue class9.3 %
A047451Numbers that are congruent to {0, 6} mod 8residue class12.3 %
A047452Numbers that are congruent to {1, 6} mod 8residue class21.1 %
A047453Numbers that are congruent to {0, 1, 2, 3, 4} mod 8residue class7.3 %
A047454Numbers that are congruent to {1, 2, 3, 4} mod 8residue class11.7 %
A047455Numbers that are congruent to {2, 3, 4} mod 8residue class14.4 %
A047456Numbers that are congruent to {0, 2, 3, 4} mod 8residue class9.3 %
A047457Numbers that are congruent to {3, 4} mod 8residue class15.0 %
A047458Numbers that are congruent to {0, 3, 4} mod 8residue class8.0 %
A047459Numbers that are congruent to {1, 3, 4} mod 8residue class15.2 %
A047460Numbers that are congruent to {0, 1, 3, 4} mod 8residue class9.0 %
A047461Numbers that are congruent to {1, 4} mod 8residue class22.6 %
A047467Numbers that are congruent to {0, 2} mod 8residue class18.6 %
A047522Numbers that are congruent to {1, 7} mod 8residue class22.0 %
A047791Numbers n such that n plus digit sum of n (A007953) equals a primedigit rule19.9 %
A047845a(n) = (m-1)/2, where m is the n-th odd nonprime (A014076(n))complement9.8 %
A047915a(n) = 3*n^2-2*n+6polynomial100.0 %
A048058a(n) = n^2 + n + 11polynomial100.0 %
A048059Primes of the form k^2 + k + 11primes100.0 %
A048097Numbers k such that k^2 + k + 11 is primeprime values20.0 %
A048098Numbers k that are sqrt(k)-smooth: if p | k then p^2 <= k when p is primesmooth17.6 %
A048103Numbers not divisible by p^p for any prime pmultiplicative11.8 %
A048109Numbers having equally many squarefree and nonsquarefree divisors; number of unitary divisors of n (A034444) = number of non-unitary divisors of n (A048105)divisor functions21.5 %
A048161Primes p such that q = (p^2 + 1)/2 is also a primeprimes45.5 %
A048521Primes expressible as the sum of an integer plus its digit sumprimes23.8 %
A048701List of binary palindromes of even length (written in base 10)binary rule87.8 %
A048988Primes of the form 4*k^2 + 4*k + 59primes100.0 %
A048989Numbers k such that pi(k) is primeprimes11.5 %
A049001a(n) = prime(n)^2 - 2primes100.0 %
A049039Geometric Connell sequence: 1 odd, 2 even, 4 odd, 8 even, ..block14.3 %
A049068Complement of quarter-squares (A002620)complement9.6 %
A049097Primes p such that p+1 is squarefreeprimes31.5 %
A049231Primes p such that p - 2 is squarefreeprimes24.8 %
A049233Primes p such that p + 2 is squarefreeprimes25.8 %
A049282Primes p such that both p-2 and p+2 are squarefreeprimes28.0 %
A049422Numbers k such that k^2 + 3 is primeprime values20.7 %
A049423Primes of the form k^2 + 3primes100.0 %
A049445Numbers k with the property that the number of 1's in binary expansion of k (see A000120) divides kbinary rule19.0 %
A049480a(n) = (2*n-1)*(n^2 -n +6)/6polynomial100.0 %
A049481Primes p such that p + 30 is also primeprimes33.9 %
A049482Primes p such that p + 210 is also primeprimes32.0 %
A049488Primes p such that p+16 is primeprimes47.2 %
A049489Primes p such that p + 32 is also primeprimes47.2 %
A049490a(n) and a(n)+64 both primeprimes47.3 %
A049492Primes p such that p+4 and p+16 are also primesprimes65.9 %
A049532Numbers k such that k^2 + 1 is not squarefreepolynomial25.0 %
A050265Primes of the form 2*n^2 + 11primes100.0 %
A050384Nonprimes such that n and phi(n) are relatively primemultiplicative19.5 %
A050408a(n) = (117*n^2 - 99*n + 2)/2polynomial100.0 %
A050435a(n) = composite(composite(n)), where composite = A002808, composite numberscomplement10.9 %
A050695Composite numbers k such that none of the prime factors of k is a substring of kdigit rule14.1 %
A050795Numbers n such that n^2 - 1 is expressible as the sum of two nonzero squares in at least one wayquadratic form36.4 %
A050813Numbers n not palindromic in any base b, 2 <= b <= 10digit rule9.8 %
A050931Numbers having a prime factor congruent to 1 mod 6multiplicative11.6 %
A050936Sum of two or more consecutive prime numbersprimes13.8 %
A051004Numbers divisible both by their individual digits and by the sum of their digitsdigit rule19.3 %
A05103811-smooth numbers: numbers whose prime divisors are all <= 11smooth98.7 %
A051270Numbers that are divisible by exactly 5 different primesmultiplicative20.2 %
A051283Numbers k such that if one writes k = Product p_i^e_i (p_i primes) and P = max p_i^e_i, then k/P > Pmultiplicative17.9 %
A051416Primes whose digits are composite; primes having only {4, 6, 8, 9} as digitsprimes38.2 %
A051507Primes p such that p*q+2 is prime, where q is next prime after pprimes45.9 %
A05162412-gonal (or dodecagonal) numbers: a(n) = n*(5*n-4)polynomial100.0 %
A051634Strong primes: prime(k) > (prime(k-1) + prime(k+1))/2primes29.4 %
A051635Weak primes: prime(n) < (prime(n-1) + prime(n+1))/2primes29.9 %
A051645Primes p such that 30*p+1 is also primeprimes35.5 %
A051647Primes p such that 210*p + 1 is also primeprimes34.3 %
A051653Primes p such that 2310*p + 1 is also primeprimes34.8 %
A051654Primes p such that 30030*p + 1 is also primeprimes34.7 %
A051677Tetrahedron-tree numbers: a(n)=sum(b(m),m=1..n), b(m)=1, 1,3, 1,3,6, 1,3,6,10,..., 1,2,...,i*(i+1)2summatory69.4 %
A05168211-gonal (or hendecagonal) numbers: a(n) = n*(9*n-7)/2polynomial100.0 %
A051750Primes whose cubes lack zerosprimes34.6 %
A05186513-gonal (or tridecagonal) numbers: a(n) = n*(11*n - 9)/2polynomial100.0 %
A05186614-gonal (or tetradecagonal) numbers: a(n) = n*(6*n-5)polynomial100.0 %
A05186715-gonal (or pentadecagonal) numbers: n*(13n-11)/2polynomial100.0 %
A05186816-gonal (or hexadecagonal) numbers: a(n) = n*(7*n-6)polynomial100.0 %
A051942a(n) = n*(n+1)/2 - 45polynomial100.0 %
A052018Numbers k with the property that the sum of the digits of k is a substring of kdigit rule20.5 %
A052026Composites base 10 that remain composite in all bases b, 2<=b<=10, expansions interpreted as decimal numbersdigit rule11.6 %
A052034Primes such that the sum of the squares of their digits is also a primeprimes35.9 %
A052040Numbers whose square is zerolessdigit rule12.2 %
A052042Primes that lack the digit zero in the decimal expansion of their squaresprimes29.5 %
A052044Numbers k such that k^3 lacks the digit zero in its decimal expansiondigit rule15.7 %
A052214Numbers n with prime signature(n) = prime signature(n+1) = prime signature(n+2)multiplicative42.4 %
A052223Numbers whose sum of digits is 9digit rule13.0 %
A052291Primes p such that 4p^2 + 1 is also primeprimes46.0 %
A052382Numbers without 0 in the decimal expansion, colloquial 'zeroless numbers'digit rule10.5 %
A052383Numbers without 1 as a digitdigit rule9.3 %
A052404Numbers without 2 as a digitdigit rule10.4 %
A052405Numbers without 3 as a digitdigit rule8.1 %
A052406Numbers without 4 as a digitdigit rule10.5 %
A052413Numbers without 5 as a digitdigit rule9.6 %
A052414Numbers without 6 as a digitdigit rule13.1 %
A052419Numbers without 7 as a digitdigit rule11.9 %
A052421Numbers without 8 as a digitdigit rule8.0 %
A052485Weak numbers (i.e., not powerful (1)): there is a prime p where p|n is true but p^2|n is not truemultiplicative9.6 %
A052499If n is in the sequence then so are 2n and 4n-1self-referential11.6 %
A052905a(n) = (n^2 + 7*n + 2)/2polynomial100.0 %
A053176Primes p such that 2p+1 is compositeprimes24.0 %
A053182Primes p such that p^2 + p + 1 is primeprimes50.4 %
A053184Primes p such that p^2+p-1 is primeprimes39.5 %
A053224Numbers k for which sigma(k) < sigma(k+1)divisor functions16.0 %
A053432Numbers with digits in alphabetical order (in English)digit rule15.7 %
A053580Primes having only {0, 6, 8, 9} as digitsprimes38.7 %
A053696Numbers that can be represented as a string of three or more 1's in a base >= 2powers99.4 %
A053698a(n) = n^3 + n^2 + n + 1polynomial100.0 %
A053755a(n) = 4*n^2 + 1polynomial100.0 %
A053868Numbers whose sum of proper divisors is odddivisor functions17.9 %
A054000a(n) = 2*n^2 - 2polynomial100.0 %
A054211Numbers k such that k concatenated with k-1 is primedigit rule26.3 %
A054353Partial sums of Kolakoski sequence A000002summatory11.8 %
A054385Beatty sequence for e/(e-1); complement of A022843Beatty12.1 %
A054386Beatty sequence for Pi/(Pi-1); complement of A022844Beatty11.6 %
A054402Numbers that are the sum of a positive square and a positive cube in more than one waypowers46.0 %
A054552a(n) = 4*n^2 - 3*n + 1polynomial100.0 %
A054554a(n) = 4*n^2 - 10*n + 7polynomial100.0 %
A054556a(n) = 4*n^2 - 9*n + 6polynomial100.0 %
A054567a(n) = 4*n^2 - 7*n + 4polynomial100.0 %
A054569a(n) = 4*n^2 - 6*n + 3polynomial100.0 %
A054683Numbers whose sum of digits is evendigit rule10.1 %
A054684Numbers whose sum of digits is odddigit rule11.0 %
A054741Numbers m such that totient(m) < cototient(m)divisor functions10.2 %
A054753Numbers which are the product of a prime and the square of a different prime (p^2 * q)multiplicative27.4 %
A054965Beatty sequence for log_3(10), i.e., for 1/log_10(3); so largest exponent of 3 which produces an n-digit decimal numberBeatty14.0 %
A054966Numbers that are congruent to {0, 1, 8} mod 9residue class16.0 %
A054967Numbers that are congruent to {0, 1, 9} mod 10residue class18.2 %
A055039Numbers of the form 2^(2i+1)*(8j+7)residue class23.7 %
A055040Numbers of the form 3^(2i+1)*(3*j+2)residue class19.4 %
A055048Numbers of the form 9^i*(3*j+2)residue class19.4 %
A055112a(n) = n*(n+1)*(2*n+1)polynomial100.0 %
A055393Sum of a square and a nonnegative cube in more than one waypowers45.8 %
A055437a(n) = 10*n^2+npolynomial100.0 %
A055438a(n) = 100*n^2 + npolynomial100.0 %
A055494Numbers k such that k^2 - k + 1 is primeprime values25.0 %
A055638Numbers k for which sigma(k^2) is primedivisor functions50.4 %
A055998a(n) = n*(n+5)/2polynomial100.0 %
A055999a(n) = n*(n + 7)/2polynomial100.0 %
A056000a(n) = n*(n+9)/2polynomial100.0 %
A056020Numbers that are congruent to +-1 mod 9residue class10.6 %
A056081Numbers that are congruent to {1, 26} mod 27residue class14.9 %
A056115a(n) = n*(n+11)/2polynomial100.0 %
A056119a(n) = n*(n+13)/2polynomial100.0 %
A056121a(n) = n*(n + 15)/2polynomial100.0 %
A056126a(n) = n*(n + 17)/2polynomial100.0 %
A056220a(n) = 2*n^2 - 1polynomial100.0 %
A056237a(n) = 2*n^2 + 9*n - 5polynomial100.0 %
A056520a(n) = (n + 2)*(2*n^2 - n + 3)/6polynomial100.0 %
A056524Palindromes with even number of digitsdigit rule94.5 %
A056578a(n) = 1 + 2*n + 3*n^2 + 4*n^3polynomial100.0 %
A056709Naught-y primes, primes with noughts (or zeros)primes25.4 %
A056809Numbers k such that k, k+1 and k+2 are products of two primesmultiplicative54.5 %
A056815Primes with prime "look and say" descriptionsprimes43.0 %
A056867Nilpotent numbers: n such that every group of order n is nilpotentmultiplicative14.5 %
A056868Numbers that are not nilpotent numbersmultiplicative12.5 %
A056874Primes of form x^2+xy+3y^2, discriminant -11quadratic form30.5 %
A056899Primes of the form k^2 + 2primes100.0 %
A056905Primes of the form k^2 + 5primes100.0 %
A056906Numbers k such that 36*k^2 + 5 is primeprime values21.1 %
A056908Numbers k such that 36*k^2 + 36*k + 13 is primeprime values22.0 %
A056909Primes of the form k^2+6primes100.0 %
A057104The non-octal numbers: numbers containing an 8 or 9 (they cannot be mistaken for octal numbers)digit rule9.5 %
A057165Indices of addition steps in Recamán's sequence A005132self-referential13.5 %
A057436Contains digits 1 through 6 onlydigit rule11.5 %
A057604Primes of the form 4*k^2 + 163primes100.0 %
A057813a(n) = (2*n+1)*(4*n^2+4*n+3)/3polynomial100.0 %
A058331a(n) = 2*n^2 + 1polynomial100.0 %
A058369Numbers k such that k and k^2 have same digit sumdigit rule33.8 %
A059094Numbers whose sum of digits is a cubedigit rule11.1 %
A059100a(n) = n^2 + 2polynomial100.0 %
A059269Numbers m for which the number of divisors, tau(m), is divisible by 3divisor functions16.9 %
A059325Numbers n such that 6n + 5 is primeprime values16.3 %
A059404Numbers with different exponents in their prime factorizationsmultiplicative13.0 %
A059425Primes of form n^2 + 19n + 17primes100.0 %
A059456Unsafe primes: primes not in A005385primes23.5 %
A059531Beatty sequence for 1 + 1/PiBeatty11.0 %
A059532Beatty sequence for 1 + PiBeatty18.4 %
A059535Beatty sequence for Pi^2/6, or zeta(2)Beatty12.4 %
A059536Beatty sequence for zeta(2)/(zeta(2)-1)Beatty15.2 %
A059537Beatty sequence for zeta(3)Beatty10.5 %
A059538Beatty sequence for zeta(3)/(zeta(3)-1)Beatty21.3 %
A059539Beatty sequence for 3^(1/3)Beatty11.5 %
A059540Beatty sequence for 3^(1/3)/(3^(1/3)-1)Beatty17.1 %
A059541Beatty sequence for 1 + log(2)Beatty12.4 %
A059542Beatty sequence for 1 + 1/log(2)Beatty15.0 %
A059543Beatty sequence for log(3)Beatty10.0 %
A059544Beatty sequence for log(3)/(log(3)-1)Beatty25.7 %
A059545Beatty sequence for log(10)Beatty14.7 %
A059546Beatty sequence for log(10)/(log(10)-1)Beatty12.9 %
A059547Beatty sequence for 1 + 1/log(3)Beatty13.4 %
A059548Beatty sequence for 1 + log(3)Beatty14.0 %
A059549Beatty sequence for 1 + 1/log(10)Beatty11.6 %
A059550Beatty sequence for 1 + log(10)Beatty17.2 %
A059551Beatty sequence for Gamma(1/3)Beatty15.6 %
A059552Beatty sequence for Gamma(1/3)/(Gamma(1/3)-1)Beatty12.1 %
A059553Beatty sequence for Gamma(2/3)Beatty11.0 %
A059554Beatty sequence for Gamma(2/3)/(Gamma(2/3)-1)Beatty18.1 %
A059556Beatty sequence for 1 + 1/gammaBeatty15.8 %
A059557Beatty sequence for 1 + gamma^2, (gamma is the Euler-Mascheroni constant A001620)Beatty11.1 %
A059559Beatty sequence for 1 + log(1/gamma), (gamma is the Euler-Mascheroni constant A001620)Beatty11.9 %
A059560Beatty sequence for 1 - 1/log(gamma)Beatty15.9 %
A059562Beatty sequence for log(Pi)/(log(Pi)-1)Beatty23.3 %
A059563Beatty sequence for e + 1/eBeatty16.8 %
A059564Beatty sequence for (e^2 + 1)/(e^2 - e + 1)Beatty11.8 %
A059566Beatty sequence for e^gamma/(e^gamma-1)Beatty14.5 %
A059567Beatty sequence for 1 - log(log(2))Beatty11.3 %
A059568Beatty sequence for 1 - 1/log(log(2))Beatty17.9 %
A059708Numbers k such that all digits have same paritydigit rule15.5 %
A059722a(n) = n*(2*n^2 - 2*n + 1)polynomial100.0 %
A059845a(n) = n*(3*n + 11)/2polynomial100.0 %
A060163a(n) = (n^3 + 5*n + 18)/6polynomial100.0 %
A060254Primes which are the sum of two consecutive composite numbersprimes23.9 %
A060544Centered 9-gonal (also known as nonagonal or enneagonal) numbers. Every third triangular number, starting with a(1)=1polynomial100.0 %
A060785a(n) = 3*(n - 2)*(5*n -11)polynomial100.0 %
A060787a(n) = 18*(n - 2)*(2*n - 5)polynomial100.0 %
A060820a(n) = (2*n-1)^2 + (2*n)^2polynomial100.0 %
A060834a(n) = 6*n^2 + 6*n + 31polynomial100.0 %
A060844Primes of the form 6*k^2 + 6*k + 31primes100.0 %
A060874Intrinsic 4-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some basedigit rule29.2 %
A060879Intrinsic 9-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some basedigit rule59.9 %
A060947Intrinsic 10-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some basedigit rule82.3 %
A061241Prime numbers == 7 (mod 9)primes42.7 %
A061242Primes of the form 9*k - 1primes42.7 %
A061246Prime having only {0, 1, 4, 9} as digitsprimes35.5 %
A061247Primes having only {0, 1, 8} as digitsprimes40.2 %
A061346Odd numbers that are neither primes nor prime powersmultiplicative21.0 %
A061372Primes having only 0,4,6,8,9 as digitsprimes39.1 %
A061384Numbers n such that sum of digits = number of digitsdigit rule23.8 %
A061426Geometric mean of the digits = 2. In other words, the product of the digits is = 2^k where k is the number of digitsdigit rule26.9 %
A061550a(n) = (2*n+1)*(2*n+3)*(2*n+5)polynomial100.0 %
A061673Even numbers k such that k+1 and k-1 are both compositecomplement11.1 %
A061681a(0)=1; a(n) = a(n-1) + lead(a(n-1)) for n > 0 where for an integer x lead(x) is the leading digit in base 10self-referential10.4 %
A061722a(n) = 10*n^2 + 7polynomial100.0 %
A061779Primes p such that q-p = 22, where q is the next prime after pprimes54.1 %
A061792a(n) = 49*(n*(n+1)/2) + 6polynomial100.0 %
A061793a(n) = 25*n*(n + 1)/2 + 3polynomial100.0 %
A061804a(n) = 2*n*(2*n^2 + 1)polynomial100.0 %
A062025a(n) = n*(13*n^2 - 7)/6polynomial100.0 %
A062123a(n) = (9n^2 + 9n + 4)/2polynomial100.0 %
A062284Primes p such that p + 50 is also primeprimes45.0 %
A062324Primes p such that p^2 + 4 is also primeprimes45.9 %
A062326Primes p such that p^2 - 2 is also primeprimes39.8 %
A062336Primes whose sum of digits is a multiple of 7primes39.1 %
A062338Primes whose sum of digits is a multiple of 4primes34.0 %
A062340Primes whose sum of digits is a multiple of 5primes35.0 %
A062350Primes having only {1, 2, 3} as digitsprimes29.9 %
A062503Squarefree numbers squaredmultiplicative100.0 %
A062634Numbers k such that every divisor of k contains the digit 1divisor functions23.2 %
A062713Numbers k such that the sum of the digits of k is a prime factor of kdigit rule33.5 %
A062721Numbers k such that k is a product of two primes and k-2 is primemultiplicative40.2 %
A062737Primes p such that 4p-1 is also primeprimes47.8 %
A062783a(n) = 3*n*(4*n-1)polynomial100.0 %
A062786Centered 10-gonal numberspolynomial100.0 %
A062800Primes of form 100*k + 1primes53.1 %
A062832Numbers k such that k and k+2 have the same number of divisorsmultiplicative22.1 %
A062996Numbers whose sum of digits is greater than or equal to its product of digitsdigit rule8.9 %
A062997Numbers whose sum of digits is strictly greater than its product of digitsdigit rule8.9 %
A062998Numbers whose sum of digits is less than or equal to its product of digitsdigit rule10.5 %
A063037Numbers without 3 consecutive equal binary digitsbinary rule10.2 %
A063464Numbers k such that omega(k) = omega(k+2), where omega(k) is the number of distinct prime divisors of kmultiplicative14.7 %
A063465Number k such that omega(k) = omega(k+3), where omega(k) is the number of distinct prime divisors of kmultiplicative16.6 %
A063472Primes of the form 666*k - 1primes68.9 %
A063488a(n) = (2*n-1)*(n^2 -n +2)/2polynomial100.0 %
A063489a(n) = (2*n-1)*(5*n^2-5*n+6)/6polynomial100.0 %
A063490a(n) = (2*n - 1)*(7*n^2 - 7*n + 6)/6polynomial100.0 %
A063491a(n) = (2*n - 1)*(3*n^2 - 3*n + 2)/2polynomial100.0 %
A063492a(n) = (2*n - 1)*(11*n^2 - 11*n + 6)/6polynomial100.0 %
A063493a(n) = (2*n-1)*(13*n^2-13*n+6)/6polynomial100.0 %
A063494a(n) = (2*n - 1)*(7*n^2 - 7*n + 3)/3polynomial100.0 %
A063495a(n) = (2*n-1)*(5*n^2-5*n+2)/2polynomial100.0 %
A063496a(n) = (2*n - 1)*(8*n^2 - 8*n + 3)/3polynomial100.0 %
A063521a(n) = n*(7*n^2-4)/3polynomial100.0 %
A063522a(n) = n*(5*n^2 - 3)/2polynomial100.0 %
A063523a(n) = n*(8*n^2 - 5)/3polynomial100.0 %
A063637Primes p such that p+2 is a semiprimeprimes36.0 %
A063638Primes p such that p-2 is a semiprimeprimes34.8 %
A063909Primes p such that 2*p - 5 is also primeprimes45.3 %
A063910Primes p such that 2*p - 7 is also primeprimes45.8 %
A063911Primes p such that 2*p - 9 is also primeprimes36.3 %
A063912Primes p such that 2*p - 11 is also primeprimes46.9 %
A063913Primes p such that 2*p - 13 is also primeprimes47.1 %
A064052Not sqrt(n)-smooth: some prime factor of n is > sqrt(n)smooth9.5 %
A064150Numbers divisible by the sum of their ternary digitsdigit rule19.7 %
A064194a(2n) = 3*a(n), a(2n+1) = 2*a(n+1)+a(n), with a(1) = 1self-referential56.7 %
A064225a(n) = (9*n^2 + 5*n + 2)/2polynomial100.0 %
A064226a(n) = (9*n^2 + 13*n + 6)/2polynomial100.0 %
A064437a(1)=1, a(n) = a(n-1) + 3 if n is already in the sequence, a(n) = a(n-1) + 2 otherwiseself-referential15.0 %
A064481Numbers which are divisible by the sum of their base-5 digitsdigit rule18.6 %
A064608Partial sums of A034444: sum of number of unitary divisors from 1 to nsummatory26.4 %
A064700Numbers k that are divisible by the multiplicative digital root of kdigit rule20.7 %
A064761a(n) = 15*n^2polynomial100.0 %
A064762a(n) = 21*n^2polynomial100.0 %
A064763a(n) = 28*n^2polynomial100.0 %
A065496Numbers n such that sigma(n) is a nontrivial power, i.e., sigma(n) = a^b where a and b are greater than 1divisor functions44.3 %
A065508Primes p such that p^2 - p + 1 is primeprimes50.3 %
A065877Non-Niven (or non-Harshad) numbers: numbers which are not a multiple of the sum of their digitsdigit rule8.3 %
A066031Composite numbers n the sum of whose prime factors divides n, but which are not themselves powers of primesmultiplicative36.1 %
A066049Numbers k such that 2*k^2 - 1 is a primeprime values20.8 %
A066343Beatty sequence for log_2(10)Beatty17.1 %
A066344Beatty sequence for log_5(10)Beatty11.4 %
A066436Primes of the form 2*n^2 - 1primes100.0 %
A066649Primes of the form a^2 + b^3 with a, b > 0primes46.1 %
A066938Primes of the form p*q+p+q, where p and q are primesprimes38.2 %
A067076Numbers k such that 2*k + 3 is a primeprime values16.0 %
A067201Numbers k such that k^2 + 2 is primeprime values28.9 %
A067251Numbers with no trailing zeros in decimal representationresidue class10.6 %
A067256Numbers k such that k, 2*k+1, 3*k+2 are primesprimes64.3 %
A067259Cubefree numbers which are not squarefreemultiplicative17.9 %
A067389a(n) = 3*n^3 + 2*n^2 + npolynomial100.0 %
A067611Numbers of the form 6xy +- x +- y, where x, y are positive integerscomplement9.5 %
A067705a(n) = 11*n^2 + 22*npolynomial100.0 %
A067707a(n) = 3*n^2 + 12*npolynomial100.0 %
A067724a(n) = 5*n^2 + 10*npolynomial100.0 %
A067725a(n) = 3*n^2 + 6*npolynomial100.0 %
A067726a(n) = 6*n^2 + 12*npolynomial100.0 %
A067727a(n) = 7*n^2 + 14*npolynomial100.0 %
A067728a(n) = 2*n^2 + 8*npolynomial100.0 %
A067885Products of exactly 6 distinct primesmultiplicative29.5 %
A067889Primes sandwiched between two numbers having same number of divisorsprimes44.1 %
A068228Primes congruent to 1 (mod 12)primes40.2 %
A068229Primes congruent to 7 (mod 12)primes40.2 %
A068231Primes congruent to 11 mod 12primes40.0 %
A068601a(n) = n^3 - 1polynomial100.0 %
A068780Composite numbers n such that n+1 is also compositecomplement11.2 %
A068781Lesser of two consecutive numbers each divisible by a squaremultiplicative24.9 %
A069059Numbers k such that k and sigma(k) are not relatively primedivisor functions12.6 %
A069072a(n) = (2n+1)*(2n+2)*(2n+3)polynomial100.0 %
A069099Centered heptagonal numberspolynomial100.0 %
A069125a(n) = (11*n^2 - 11*n + 2)/2polynomial100.0 %
A06927211-almost primes (generalization of semiprimes)multiplicative22.5 %
A06927312-almost primes (generalization of semiprimes)multiplicative23.3 %
A06927413-almost primes (generalization of semiprimes)multiplicative24.6 %
A069346Primes of the form n - Omega(n), where Omega(n) is the number of prime factors of n, A001222(n)primes26.7 %
A069477a(n) = 60*n^2 + 180*n + 150polynomial100.0 %
A069977Numbers k such that k and k+2 are squarefreemultiplicative19.6 %
A070552Semiprimes k such that k+1 is also a semiprimemultiplicative31.9 %
A070938Harshad numbers which terminate in their digital sumdigit rule25.3 %
A071139Numbers k such that the sum of distinct primes dividing k is divisible by the largest prime dividing kmultiplicative23.1 %
A071229a(n) = n*(14*n^2 - 21*n + 13)/6polynomial100.0 %
A071230a(n) = n*(6*n^2 - 7*n + 3)/2polynomial100.0 %
A071233a(n) = 2*(n-1)*(n^2 + 1)polynomial100.0 %
A071355a(n) = 2*n^2 + 11*n + 12polynomial100.0 %
A071395Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers)divisor functions53.8 %
A071403Which squarefree number is prime? a(n)-th squarefree number equals n-th primeprimes21.2 %
A071696Greater members of twin prime pairs of form (4*k+1,4*k+3), k>0primes51.7 %
A071698Lesser members of twin prime pairs of form (4*k+3, 4*k+5), k >= 0primes52.3 %
A072055a(n) = 2*prime(n)+1primes34.6 %
A072202Same numbers of prime factors of forms 4*k+1 and 4*k+3, counted with multiplicitymultiplicative16.0 %
A072225Numbers k such that prime(k) + prime(k+1) + prime(k+2) is primeprimes19.0 %
A072437Numbers with no prime factors of form 4*k+3multiplicative15.7 %
A072587Numbers having at least one prime factor with an even exponentmultiplicative15.8 %
A072682Numbers congruent to {3, 36, 54, 57} mod 60residue class23.1 %
A072774Powers of squarefree numberspowers10.7 %
A072833Numbers that are congruent to 0, 5, 8, 9 mod 12residue class21.4 %
A072859Primes p for which the period of 1/p is primeprimes47.8 %
A072960Numbers using only the curved digits 0, 3, 6, 8 and 9digit rule13.0 %
A072961Numbers using only the digits 2 and 5, that are both curved and straightdigit rule15.2 %
A072978Numbers of the form m * 2^bigomega(m), where m>1 is odd and bigomega(m) = A001222(m), the number of prime factors of mmultiplicative14.0 %
A073085Numbers k such that 210*k+1 is primeprime values16.3 %
A073102Primes of the form 210n + 1primes62.8 %
A073121a(n) = r*a(ceiling(n/2)) + s*a(floor(n/2)) with a(1)=1 and (r,s)=(2,2)self-referential100.0 %
A073247Squarefree numbers k such that k-1 and k+1 are not squarefreemultiplicative20.4 %
A073492Numbers having at least one prime gap in their factorizationmultiplicative10.5 %
A073493Numbers having exactly one prime gap in their factorizationmultiplicative14.2 %
A073577a(n) = 4*n^2 + 4*n - 1polynomial100.0 %
A074627Numbers n such that sigma(n) is divisible by 6divisor functions9.2 %
A074741Sum of squares of gaps between consecutive primessummatory43.0 %
A074742a(n) = (n^3 + 6n^2 - n + 12)/6polynomial100.0 %
A074822Primes p such that p + 4 is prime and p == 9 (mod 10)primes57.9 %
A074832Primes whose binary reversal is also primeprimes34.7 %
A074940Numbers having at least one 2 in their ternary representationdigit rule9.7 %
A074969Numbers with six distinct prime divisorsmultiplicative22.8 %
A075109Odd perfect powers (1 together with numbers m^k, m odd, k >= 2)powers99.7 %
A075432Primes with no squarefree neighborsprimes33.6 %
A075592Numbers n such that number of distinct prime divisors of n is a divisor of nmultiplicative13.5 %
A075745Numbers n such that 210*n + 13 is primeprime values16.0 %
A075746Numbers n such that 210*n-13 is primeprime values16.6 %
A075747Numbers n such that 210*n + 17 is primeprime values16.4 %
A075748Numbers k such that 210*k-17 is primeprime values16.7 %
A076056Primes which when read backwards are composite numbersprimes24.5 %
A076339Primes of the form 512*k+1primes64.2 %
A076354Numbers n such that 210*n-1 is primeprime values16.5 %
A076355Numbers n such that 210*n + 11 is primeprime values16.7 %
A076356Numbers n such that 210*n-11 is primeprime values15.5 %
A076727Primes of the form x^2 + (x+3)^2primes100.0 %
A077064Squarefree numbers of form prime - 1primes33.0 %
A077068Semiprimes of the form prime + 1primes47.8 %
A077414a(n) = n*(n - 1)*(n + 2)/2polynomial100.0 %
A077415a(n) = n*(n+2)*(n-2)/3polynomial100.0 %
A077436Let B(n) be the sum of binary digits of n. This sequence contains n such that B(n) = B(n^2)binary rule28.5 %
A077477Least positive integers not excluded by the rule that if n is present then 2n+1 and 3n+1 are not allowedself-referential14.4 %
A077654Composites k such that 2k+1 is also compositecomplement10.8 %
A077717Primes which can be expressed as a sum of distinct powers of 3primes38.1 %
A078309Numbers that are congruent to {1, 4, 7} mod 10residue class23.4 %
A078358Non-oblong numbers: Complement of A002378complement9.5 %
A078370a(n) = 4*(n+1)*n + 5polynomial100.0 %
A078371a(n) = (2*n+5)*(2*n+1)polynomial100.0 %
A078402Numbers k such that k^2 + 5 is primeprime values21.1 %
A078494Primes occurring only once in their decadeprimes27.1 %
A078633Smallest number of sticks of length 1 needed to construct n squares with sides of length 1polynomial13.8 %
A078649Numbers n such that A000002(n)=A000002(n+1) where A000002 is the Kolakoski sequenceself-referential16.2 %
A078972Brilliant numbers: semiprimes (products of two primes, A001358) whose prime factors have the same number of decimal digitsmultiplicative35.1 %
A079138Primes of the form k^2 + 7primes100.0 %
A079498Numbers whose sum of digits in base b gives 0 (mod b), for b = 3digit rule16.2 %
A079523Utterly odd numbers: numbers whose binary representation ends in an odd number of onesbinary rule20.6 %
A079545Primes of the form x^2 + y^2 + 1 with x,y >= 0primes38.5 %
A079588a(n) = (n+1)*(2*n+1)*(4*n+1)polynomial100.0 %
A079651Primes having only {1, 4, 7} as digitsprimes33.5 %
A079652Prime numbers using only the curved digits 0, 3, 6, 8 and 9primes32.6 %
A080075Proth numbers: of the form k*2^m + 1 for k odd, m >= 1 and 2^m > kpowers100.0 %
A080147Positions of primes of the form 4*k+1 (A002144) among all primes (A000040)primes13.0 %
A08019713-smooth numbers: numbers whose prime divisors are all <= 13smooth93.1 %
A080228Numbers containing the digits 0, 1, 2, 5 or 8 onlydigit rule14.6 %
A080663a(n) = 3*n^2 - 1polynomial100.0 %
A08068117-smooth numbers: numbers whose prime divisors are all <= 17smooth79.2 %
A08068219-smooth numbers: numbers whose prime divisors are all <= 19smooth55.6 %
A08068323-smooth numbers: numbers whose prime divisors are all <= 23smooth41.5 %
A080855a(n) = (9*n^2 - 3*n + 2)/2polynomial100.0 %
A080857a(n) = (25*n^2 - 15*n + 2)/2polynomial100.0 %
A080859a(n) = 6*n^2 + 4*n + 1polynomial100.0 %
A080860a(n) = 10*n^2 + 5*n + 1polynomial100.0 %
A080861a(n) = 15*n^2 + 6*n + 1polynomial100.0 %
A081092Primes having a prime number of 1's in their binary representationprimes31.4 %
A081311Numbers that can be written as sum of a prime and an 3-smooth numbersmooth10.9 %
A081330Numbers that can be written as sum of two 3-smooth numberssmooth61.6 %
A081605Numbers having at least one 0 in their ternary representationdigit rule9.6 %
A081759Numbers k such that 5*k+6 is primeprime values24.5 %
A082040a(n) = 9*n^2 + 3*n + 1polynomial100.0 %
A082041a(n) = 16*n^2 + 4*n + 1polynomial100.0 %
A082108a(n) = 4*n^2 + 6*n + 1polynomial100.0 %
A082111a(n) = n^2 + 5*n + 1polynomial100.0 %
A082112a(n) = 4*n^2 + 10*n + 1polynomial100.0 %
A082246Primes that are the sum of 7 consecutive primesprimes52.4 %
A082369Numbers congruent to 13 mod 30residue class43.7 %
A082885Primes followed by a larger-than-average prime gapprimes33.7 %
A082977Numbers that are congruent to {0, 1, 3, 5, 6, 8, 10} mod 12residue class11.7 %
A083022Numbers n such that 4*n^2 - 3 is primeprime values18.9 %
A083026Numbers that are congruent to {0, 2, 4, 5, 7, 9, 11} mod 12residue class12.0 %
A083028Numbers that are congruent to {0, 2, 3, 5, 7, 8, 11} mod 12residue class15.8 %
A083030Numbers that are congruent to {0, 4, 7} mod 12residue class22.2 %
A083031Numbers that are congruent to {0, 3, 7} mod 12residue class23.7 %
A083032Numbers that are congruent to {0, 4, 7, 10} mod 12residue class10.2 %
A083033Numbers that are congruent to {0, 2, 3, 5, 7, 9, 10} mod 12residue class15.8 %
A083034Numbers that are congruent to {0, 1, 3, 5, 7, 8, 10} mod 12residue class11.7 %
A083089Numbers that are congruent to {0, 2, 4, 6, 7, 9, 11} mod 12residue class20.1 %
A083120Numbers that are congruent to {0, 2, 4, 5, 7, 9, 10} mod 12residue class8.1 %
A084367a(n) = n*(2*n+1)^2polynomial100.0 %
A084377a(n) = n^3 + 7polynomial100.0 %
A084378a(n) = n^3 + 3polynomial100.0 %
A084379a(n) = n^3 + 17polynomial100.0 %
A084380a(n) = n^3 + 2polynomial100.0 %
A084381a(n) = n^3 + 5polynomial100.0 %
A084382a(n) = n^3 + 6polynomial100.0 %
A084544Alternate number system in base 4digit rule11.2 %
A084545Alternate number system in base 5digit rule12.9 %
A084849a(n) = 1 + n + 2*n^2polynomial100.0 %
A084865Primes of the form 2x^2 + 3y^2quadratic form39.5 %
A084969Numbers whose smallest prime factor is 11multiplicative14.8 %
A084970Numbers whose smallest prime factor is 13multiplicative15.6 %
A084984Numbers containing no prime digitsdigit rule15.2 %
A084990a(n) = n*(n^2+3*n-1)/3polynomial100.0 %
A085001a(n) = (3*n+1)*(3*n+4)polynomial100.0 %
A085025a(n) = (5*n+1)*(5*n+6)polynomial100.0 %
A085026a(n) = (6*n+1)*(6*n+7)polynomial100.0 %
A085027a(n) = (4*n+3)*(4*n+7)polynomial100.0 %
A085036a(n) = (5*n+2)*(5*n+7)polynomial100.0 %
A085370Niven (or Harshad) numbers that are not divisible by 3digit rule23.6 %
A085371Non-Niven (or non-Harshad) numbers that are divisible by 3digit rule8.3 %
A085473a(n) = 6*n^2 + 3*n + 1polynomial100.0 %
A085722Numbers k such that k^2 + 1 is a semiprimemultiplicative16.7 %
A085746Numbers n such that n^2 + n + 1 is a semiprimemultiplicative17.2 %
A085780Numbers that are a product of 2 triangular numberspolynomial42.2 %
A085786a(n) = n*(2*n^2 + n + 1)/2polynomial100.0 %
A085802Numbers whose sum of digits is a semiprimedigit rule13.7 %
A085959Multiples of 37residue class9.7 %
A086005Semiprimes sandwiched between semiprimesmultiplicative50.0 %
A086006Primes p such that 2*p-1 and 2*p+1 are semiprimesprimes49.8 %
A086285Numbers k such that 1 + 2k + 3k^2 is primeprime values24.0 %
A086298Numbers n such that 1-2n+3n^2 is primeprime values23.7 %
A086303Numbers n such that n+15 is primeprime values14.9 %
A086304Numbers n such that n+6 is primeprime values25.6 %
A086381Numbers k such that p=k^2+2 and p+2 are primesprime values47.0 %
A086605a(n) = 9*n^3 - 18*n^2 + 10*npolynomial100.0 %
A086760a(n) = 8*n^2 + 88*n + 43polynomial100.0 %
A087057Smallest number whose square is larger than 2*n^2Beatty11.3 %
A087248Squarefree abundant numbersdivisor functions15.0 %
A087348a(n) = 10*n^2 - 6*n + 1polynomial100.0 %
A087363Primes having only {3, 5, 7} as digitsprimes34.5 %
A087370Numbers n such that 3n - 1 is a primeprime values18.1 %
A087444Numbers that are congruent to {1, 4} mod 9residue class22.5 %
A087446Numbers that are congruent to {1, 6} mod 15residue class29.7 %
A087475a(n) = n^2 + 4polynomial100.0 %
A087505Numbers k such that 5*k+3 is a primeprime values15.9 %
A087695Numbers n such that n + 3 and n - 3 are both primeprime values30.0 %
A087863a(n) = (n^3 + 24*n^2 + 65*n + 36)/6polynomial100.0 %
A088179Primes p such that mu(p-1) = 1; that is, p-1 is squarefree and has an even number of prime factors, where mu is the Moebius functionprimes35.3 %
A088485Numbers n such that n^2 + n - 1 and n^2 + n + 1 are twin primesprime values38.6 %
A088572Numbers n such that (2n+1)^2 - 2 is primeprime values20.6 %
A088723Numbers k with at least one divisor d>1 such that d+1 also divides kdivisor functions14.5 %
A088758Numbers k such that (4*k + 1)^2 + (4*k + 2)^2 is primeprime values22.1 %
A088759Numbers k such that (4*k+3)^2 + (4*k+2)^2 is primeprime values23.8 %
A088955Primes of the form 60*k + 1primes52.6 %
A088958Numbers n such that 60*n+1 is primeprime values17.0 %
A088967Numbers n such that n+9 is a primeprime values17.2 %
A089001Numbers k such that 2*k^2 + 1 is primeprime values19.5 %
A089008Numbers k such that 18*k^2 + 1 is primeprime values19.5 %
A089033Numbers n such that 7*n+3 is primeprime values16.4 %
A089063Numbers k such that 840*k + 175177943 is a primeprime values17.2 %
A089079Numbers n such that 7*n - 23 is primeprime values22.2 %
A089189Primes p such that p-1 is cubefreeprimes25.4 %
A089192Numbers n such that 2n - 7 is a primeprime values21.2 %
A089194Primes p such that p-1 and p+1 are cube- or higher power-freeprimes29.1 %
A089207a(n) = 4*n^3 + 2*n^2polynomial100.0 %
A089253Numbers n such that 2n - 5 is a primeprime values20.0 %
A089352Numbers that are divisible by the sum of their distinct prime factors (A008472)multiplicative23.4 %
A089373Numbers k such that k^2 - 7*k + 7 is primeprime values25.4 %
A089376Primes of the form k^2 - 7*k + 7primes100.0 %
A089438Primes p such that 6p+11 is also a primeprimes36.8 %
A089441Primes p such that 16*p+17 is a primeprimes48.3 %
A089443Primes p such that 12*p + 13 is primeprimes36.9 %
A089593Numbers k such that k^2 + 2k + 2 is primeprime values31.4 %
A089623Numbers n such that n^2 + 2n - 1 is primeprime values20.6 %
A089681Numbers n such that 3n^2 - 1 is primeprime values19.7 %
A089682Primes of the form 3*m^2 - 1primes100.0 %
A089747Numbers n such that n^2 - 2n + 5 is primeprime values21.6 %
A089953Numbers n such that 3*n+7 is primeprime values17.2 %
A090050Numbers having equal length of longest contiguous block of zeros and ones in binary expansionbinary rule14.0 %
A090187Primes of the form 11*n+2primes41.8 %
A090190Symmetric primes: an odd prime p is symmetric if there exists an odd prime q such that |p-q| = gcd(p-1,q-1)primes23.8 %
A090191Asymmetric primes: an odd prime p is asymmetric if there is no odd prime q such that |p-q|=gcd(p-1,q-1)primes38.6 %
A090197a(n) = n^3 + 6*n^2 + 6*n + 1polynomial100.0 %
A090288a(n) = 2*n^2 + 6*n + 2polynomial100.0 %
A090421Numbers that can be written in binary representation as concatenation of primesbinary rule14.3 %
A090423Primes that can be written in binary representation as concatenation of other primesprimes25.2 %
A090466Regular figurative or polygonal numbers of order greater than 2polynomial11.5 %
A090562Primes of the form 5k^2 + 5k + 1primes100.0 %
A090563Numbers k such that 5*k^2 + 5*k + 1 is primeprime values19.1 %
A090570Numbers that are congruent to {0, 1} mod 9residue class21.2 %
A090614Numbers n such that 14n+3 is primeprime values16.4 %
A090684Primes of the form 8*k^2 - 1primes100.0 %
A090685Primes of the form 8*k^2 + 1primes100.0 %
A090686Primes of the form 6n^2 - 1primes100.0 %
A090687Primes of the form 6*k^2 + 1primes100.0 %
A090693Positive numbers n such that n^2 - 2n + 2 is a primeprime values31.4 %
A090696Numbers k such that k^2 - 11 is a primeprime values25.2 %
A090698Primes of the form 2*n^2+1primes100.0 %
A090709Primes whose decimal representation is a valid number in base 6 and interpreted as such is again a primeprimes49.4 %
A090771Numbers that are congruent to {1, 9} mod 10residue class26.4 %
A090772Numbers that are congruent to {2, 8} mod 10residue class18.9 %
A090773Numbers that are congruent to {4, 6} mod 10residue class17.5 %
A091067Numbers whose odd part is of the form 4*k+3binary rule13.1 %
A091072Positive numbers k such that the Kronecker Symbol (-1 / k) > 0binary rule13.1 %
A091191Primitive abundant numbers: abundant numbers (A005101) having no abundant proper divisordivisor functions25.3 %
A091271Numbers k such that 4*k^2-11 is a primeprime values25.2 %
A091272Primes of the form n^2 - 11primes100.0 %
A091300Nonprimes of the form 6k + 1complement32.4 %
A091301Primes of the form p*q + p - q, where p and q are distinct primesprimes32.7 %
A091567Primes p such that p^2-p-1 is primeprimes40.4 %
A091633Primes having only {1, 3, 7, 9} as digitsprimes29.2 %
A091823a(n) = 2*n^2 + 3*n - 1polynomial100.0 %
A091968Primes congruent to 3 (mod 16)primes38.5 %
A091998Numbers that are congruent to {1, 11} mod 12residue class12.3 %
A091999Numbers that are congruent to {2, 10} mod 12residue class9.6 %
A092022Numbers k such that 16k + 3 is primeprime values16.9 %
A092074Primes congruent to 3 mod 17primes44.4 %
A092109Primes p such that p+3 is a semiprimeprimes40.9 %
A092168Primes congruent to 3 (modulo 19)primes45.1 %
A092178Primes congruent to 8 mod 13primes42.7 %
A092192Semiprimes that are the sum of two successive semiprimesmultiplicative34.9 %
A092207Semiprimes k such that k+2 is also a semiprimemultiplicative29.5 %
A092259Numbers that are congruent to {4, 8} mod 12residue class0.0 %
A092277a(n) = 7*n^2 + npolynomial100.0 %
A092476Numbers that are congruent to {1, 3, 9} mod 13residue class19.9 %
A092620Numbers with exactly one prime digitdigit rule16.5 %
A092621Primes with exactly one prime digitprimes33.6 %
A092968Numbers n such that 2n^2 + 11 is a primeprime values19.6 %
A093191Primes congruent to 4 mod 13primes42.6 %
A093328a(n) = 2*n^2 + 3polynomial100.0 %
A093350Primes congruent to 6 mod 13primes42.9 %
A093359Primes of the form 28*k + 1primes43.6 %
A093485a(n) = (27*n^2 + 9*n + 2)/2polynomial100.0 %
A093500a(n) = (15*n^2 + 5*n + 2)/2polynomial100.0 %
A093838Primes of the form 36n + 1primes47.3 %
A094210Numbers k such that k^2 + 3k + 1 is a primeprime values20.6 %
A094222a(n+1) = a(n) + (number of distinct prime factors of a(n)) for n>1; a(1)=1, a(2)=2self-referential12.3 %
A094407Primes of the form 16n+1primes38.2 %
A094421a(n) = n * (6*n^2 + 6*n + 1)polynomial100.0 %
A094524Primes of form 3*prime(m) + 2primes49.6 %
A094589a(1) = 1; a(n+1) = a(n) + (largest element of {a} <= n)self-referential100.0 %
A094657Primes congruent to 4 mod 17primes44.4 %
A094677Sum of digits is divisible by 10digit rule24.6 %
A095050Numbers such that all ten digits are needed to write all positive divisors in decimal representationdigit rule14.3 %
A095278Numbers k such that 4k + 3 is primeprime values16.4 %
A095796a(n) = 1 + (26*n+17+7*n^2)*n/2polynomial100.0 %
A095995Primes of the form 100n - 1primes53.1 %
A096022Numbers that are congruent to {15, 27, 39, 51} mod 60residue class22.1 %
A096376a(n) = n + (n-1)^2 + (n+1)^2polynomial100.0 %
A096689Numbers n such that 2n^2 + 3n + 3 is primeprime values19.4 %
A096691Numbers n such that 8n^2 + 6n + 3 is primeprime values19.4 %
A096777a(n) = a(n-1) + Sum_{k=1..n-1}(a(k) mod 2), a(1) = 1self-referential100.0 %
A097080a(n) = 2*n^2 - 2*n + 3polynomial100.0 %
A097102Numbers m that are the hypotenuse of exactly 13 distinct integer-sided right triangles, i.e., m^2 can be written as a sum of two squares in 13 waysquadratic form23.6 %
A097103Numbers m that are the hypotenuse of exactly 22 distinct integer-sided right triangles, i.e., m^2 can be written as a sum of two squares in 22 waysquadratic form25.7 %
A097803a(n) = 3*(2*n^2 + 1)polynomial100.0 %
A097933Primes p that divide 3^((p-1)/2) - 1primes28.5 %
A098005Beatty sequence for 1/(3 - e): a(n) = floor(n/(3-e))Beatty17.5 %
A098058Prime(n) such that 4 does not divide the difference between prime(n) and prime(n+1)primes28.1 %
A098090Numbers k such that 2k-3 is primeprime values15.1 %
A098547a(n) = n^3 + n^2 + 1polynomial100.0 %
A098603a(n) = n*(n+10)polynomial100.0 %
A098828Primes of the form 2*n^2 + 2*n - 1primes100.0 %
A098847a(n) = n*(n + 12)polynomial100.0 %
A098848a(n) = n*(n + 14)polynomial100.0 %
A098849a(n) = n*(n + 16)polynomial100.0 %
A098850a(n) = n*(n + 18)polynomial100.0 %
A098974Primes p such that q-p = 24, where q is the next prime after pprimes46.4 %
A099007Primes of the form 6n^2 - 2n - 1primes100.0 %
A099721a(n) = n^2*(2*n+1)polynomial100.0 %
A100109a(n) = n^3 - 2*n^2 + 2polynomial100.0 %
A100201Primes of the form 23*k+3primes46.5 %
A100202Primes of the form 13*k + 3primes42.7 %
A100203Primes of the form 37n+3primes49.2 %
A100207a(n) = 4 + 8*n + 10*n^2 + 4*n^3polynomial100.0 %
A100214a(n) = 4*n^3 + 4polynomial100.0 %
A100484The primes doubled; even semiprimesprimes23.0 %
A100493a(n) = n + n-th semiprimemultiplicative19.8 %
A100494Primes of the form 47*k + 3primes51.1 %
A100504a(n) = (4*n^3 + 6*n^2 + 8*n + 6)/3polynomial100.0 %
A100536a(n) = 3*n^2 - 2polynomial100.0 %
A100705a(n) = n^3 + (n+1)^2polynomial100.0 %
A100760Primes of the form 47n+5primes51.0 %
A100959Non-semiprimescomplement11.6 %
A101082Numbers n such that binary representation contains bit strings "10" and "01" (possibly overlapping)binary rule9.6 %
A101084Numbers k such that 97*k + 101 is a primeprime values24.3 %
A101095Fourth difference of fifth powers (A000584)polynomial9.7 %
A101165a(n) = (7*n^3 + 6*n^2 + 5*n) / 6polynomial100.0 %
A101444Numbers k such that (9973*k + 10007) is a primeprime values25.4 %
A101503Numbers k such that 11*k + 101 is primeprime values22.5 %
A101557Numbers k such that 101*k + 1009 is primeprime values23.7 %
A101567Numbers n such that 1009*n + 10007 is primeprime values24.8 %
A101594Numbers with exactly two distinct decimal digits, neither of which is 0digit rule22.6 %
A101780Primes of the form 100*n + 3primes53.1 %
A101813Odd Niven (or Harshad) numbers: odd numbers that are divisible by the sum of their digitsdigit rule33.9 %
A101814Even Niven (or Harshad) numbers: even numbers that are divisible by the sum of their digitsdigit rule18.8 %
A101853a(n) = n*(20 + 15*n + n^2)/6polynomial100.0 %
A101860a(n) = (3+n)*(2 + 33*n + n^2)/6polynomial100.0 %
A102083a(n) = 8*n^2 + 4*n + 1polynomial100.0 %
A102094a(n) = (2*n-1)*(2*n+1)^2polynomial100.0 %
A102130Primes of the form 8*n^2 + 4*n + 1primes100.0 %
A102148Numbers k such that 101*k + 11 is primeprime values23.4 %
A102166Numbers n such that 2*n^2 + 11*n + 101 is primeprime values23.4 %
A102271Primes of the form 3*x^2 + 7*y^2quadratic form41.1 %
A102338Numbers k such that 10k+3 is primeprime values15.9 %
A102339Numbers k such that k*10^3 + 333 is primeprime values16.9 %
A102342Numbers k such that 10k + 7 is primeprime values20.2 %
A102343Numbers k such that k*10^3 + 777 is primeprime values16.0 %
A102487Numbers in base-12 representation that can be written with decimal digitsdigit rule11.1 %
A102491Numbers whose base-20 representation can be written with decimal digitsdigit rule10.9 %
A102649Numbers n such that 11*n^2 + 11*n + 3 is primeprime values32.7 %
A102656Numbers k such that 11*k + 1 is primeprime values23.1 %
A102657Numbers k such that 11*k^2 + 11*k + 1 is primeprime values20.7 %
A102700Numbers k such that 10*k + 9 is primeprime values14.6 %
A102703Numbers k such that 100*k+99 is primeprime values16.1 %
A102711Numbers k such that 11*k + 7 is primeprime values22.0 %
A102721Numbers n such that 11*n + 13 is primeprime values22.4 %
A102731Numbers k such that 11*k + 23 is primeprime values23.1 %
A102732Primes of the form 13n+5primes42.8 %
A102733Numbers n such that 2*n + 101 is primeprime values22.6 %
A102734Primes of the form 23n+5primes46.5 %
A102768Numbers k such that 23*k + 11 is primeprime values22.7 %
A102851Primes of the form 19n + 5primes45.1 %
A102852Primes whose squares are congruent to 5 (modulo 19)primes40.2 %
A103118Numbers k such that 100*k + 57 is primeprime values16.3 %
A103215Numbers congruent to {1, 2, 5, 10, 13, 17} mod 24residue class14.8 %
A103564Primes p such that 3*p^2 + 2 is primeprimes49.2 %
A103664Primes p such that the number of divisors of p-1 is less than the number of divisors of p+1primes29.9 %
A103776Primes p such that 8*p^2 + 4*p + 1 is also primeprimes43.6 %
A103871Numbers n such that 100n + 69 is primeprime values15.6 %
A104188a(n) = 4*n*(4*n - 1)polynomial100.0 %
A104249a(n) = (3*n^2 + n + 2)/2polynomial100.0 %
A104272Ramanujan primes R_n: a(n) is the smallest number such that if x >= a(n), then pi(x) - pi(x/2) >= n, where pi(x) is the number of primes <= xprimes26.5 %
A105042Numbers n such that 10n - 1 is primeprime values21.3 %
A105043Numbers n such that 100*n - 1 is primeprime values22.5 %
A105044Numbers n such that 1000*n - 1 is primeprime values22.9 %
A105057Numbers n such that 10000 * n - 1 is primeprime values23.2 %
A105059Numbers n such that 100000n - 1 is primeprime values23.8 %
A105107Numbers n such that 10000n + 1001 is primeprime values21.6 %
A105126Primes of the form 16n+9primes38.1 %
A105127Primes of the form 32n+17primes43.3 %
A105128Primes of the form 64n+33primes47.9 %
A105129Primes of the form 128n+65primes53.0 %
A105130Primes of the form 256n+129primes58.2 %
A105131Primes of the form 512n+257primes64.2 %
A105132Primes of the form 1024n + 513primes70.4 %
A105133Numbers n such that 8n + 5 is primeprime values20.8 %
A105134Numbers n such that 16n+9 is primeprime values18.6 %
A105135Numbers n such that 32n+17 is primeprime values23.2 %
A105136Numbers n such that 64n+33 is primeprime values17.3 %
A105137Numbers n such that 128n+65 is primeprime values21.4 %
A105138Numbers n such that 256n+129 is primeprime values19.0 %
A105139Numbers k such that 512*k+257 is primeprime values24.3 %
A105140Numbers n such that 1024n+513 is primeprime values20.0 %
A105184Primes that can be written as concatenation of two primes in decimal representationprimes34.0 %
A105374a(n) = 4*n^3 + 4*npolynomial100.0 %
A105441Numbers with at least two odd prime factors (not necessarily distinct)multiplicative12.9 %
A105571Numbers m such that m - 2 and m + 2 are semiprimesmultiplicative27.5 %
A105583Numbers k such that 101*k + 997 is primeprime values24.0 %
A105679Numbers k such that 997*k + 101 is primeprime values25.2 %
A105680Numbers k such that 1009*k + 9973 is primeprime values24.8 %
A105710Numbers k such that 9973*k + 1009 is primeprime values25.3 %
A105772Numbers k such that 7*k + 2 is primeprime values32.0 %
A105773Numbers n such that 11*n + 97 is primeprime values22.7 %
A105775Numbers n such that 97*n + 11 is primeprime values23.6 %
A105854Primes of the form 20*k + 3primes42.2 %
A105961Primes p such that 20*p + 3 is primeprimes35.3 %
A106039Belgian-0 numbersdigit rule16.7 %
A106093Primes with maximal digit = 9primes26.9 %
A106110Primes having only {7, 8, 9} as digitsprimes28.2 %
A106111Primes having only {6, 7, 8, 9} as digitsprimes27.7 %
A106112Primes with minimal digit > 4primes27.9 %
A106114Primes with minimal digit > 3primes28.3 %
A106115Primes with minimal digit > 2primes25.0 %
A106116Primes without {0, 1} as digitsprimes25.3 %
A106120Primes with maximal digit > 3primes23.1 %
A106122Primes with maximal digit > 5primes23.3 %
A106124Primes with maximal digit > 7primes24.7 %
A106439Belgian-1 numbersdigit rule17.9 %
A106483Primes p such that 2*p^2 - 1 is also primeprimes39.9 %
A106518Belgian-2 numbersdigit rule15.7 %
A106564Perfect squares which are not the difference of two primespowers100.0 %
A106596Belgian-3 numbersdigit rule17.5 %
A106648a(n) = 3*n^2 + 6*n + 8polynomial100.0 %
A106690Numbers k such that 11*k - 97 is primeprime values23.1 %
A106692Numbers k such that 97*k - 11 is primeprime values23.6 %
A106695Numbers k such that 101*k - 997 is primeprime values24.1 %
A106697Numbers k such that 997*k - 101 is primeprime values25.0 %
A106699Numbers k such that 1009*k - 9973 is primeprime values24.7 %
A106700Numbers k such that 9973*k - 1009 is primeprime values25.3 %
A106839Numbers congruent to 11 mod 16residue class33.1 %
A106856Primes of the form x^2 + xy + 2y^2, with x and y nonnegativeprimes27.8 %
A106857Primes of the form x^2+xy+3y^2, with x and y nonnegativequadratic form32.0 %
A106861Primes of the form x^2+xy+4y^2, with x and y nonnegativequadratic form44.7 %
A106862Primes of the form x^2+xy+5y^2, with x and y nonnegativequadratic form30.9 %
A106866Primes of the form 2x^2+xy+3y^2, with x and y nonnegativequadratic form36.1 %
A106867Primes of the form 2*x^2 + x*y + 3*y^2quadratic form29.9 %
A106869Primes of the form x^2+xy+6y^2, with x and y nonnegativequadratic form36.2 %
A106870Primes of the form x^2+xy+7y^2, with x and y nonnegativequadratic form36.0 %
A106871Primes of the form 2x^2+xy+4y^2, with x and y nonnegativequadratic form36.6 %
A106874Primes of the form x^2+xy+8y^2, with x and y nonnegativequadratic form36.3 %
A106875Primes of the form 3x^2+2xy+3y^2, with x and y nonnegativequadratic form40.2 %
A106877Primes of the form 3x^2+xy+3y^2, with x and y nonnegativequadratic form39.4 %
A106880Primes of the form x^2+xy+9y^2, with x and y nonnegativequadratic form35.5 %
A106881Primes of the form x^2+xy+9y^2quadratic form34.8 %
A106882Primes of the form 2x^2+2xy+5y^2, with x and y nonnegativequadratic form41.7 %
A106883Primes of the form 3x^2+3xy+4y^2, with x and y nonnegativequadratic form47.9 %
A106885Primes of the form 2x^2+xy+5y^2, with x and y nonnegativequadratic form46.5 %
A106889Primes of the form 2x^2 + 5y^2quadratic form37.2 %
A106890Primes of the form x^2 + xy + 11y^2, with x and y nonnegativequadratic form29.7 %
A106892Primes of the form 3x^2+2xy+4y^2, with x and y nonnegativequadratic form39.3 %
A106894Primes of the form 3x^2+xy+4y^2, with x and y nonnegativequadratic form39.9 %
A106897Primes of the form 2x^2+xy+6y^2, with x and y nonnegativequadratic form40.0 %
A106900Primes of the form x^2+xy+12y^2, with x and y nonnegativequadratic form40.2 %
A106901Primes of the form 3x^2+3xy+5y^2, with x and y nonnegativequadratic form40.1 %
A106903Primes of the form x^2+xy+13y^2, with x and y nonnegativequadratic form39.0 %
A106905Primes of the form 2x^2+2xy+7y^2, with x and y nonnegativequadratic form36.7 %
A106907Primes of the form 4x^2+3xy+4y^2, with x and y nonnegativequadratic form49.7 %
A106910Primes of the form 2x^2+xy+7y^2, with x and y nonnegativequadratic form44.3 %
A106914Primes of the form 3x^2+2xy+5y^2, with x and y nonnegativequadratic form36.8 %
A106917Primes of the form 2x^2 + 7y^2quadratic form35.8 %
A106918Primes of the form 3x^2+xy+5y^2, with x and y nonnegativequadratic form37.6 %
A106921Primes of the form x^2+xy+15y^2, with x and y nonnegativequadratic form37.5 %
A106923Primes of the form 4x^2+xy+4y^2, with x and y nonnegativequadratic form47.1 %
A106926Primes of the form 2x^2+xy+8y^2, with x and y nonnegativequadratic form42.5 %
A106929Primes of the form x^2+xy+16y^2, with x and y nonnegativequadratic form42.2 %
A106931Primes of the form 4x^2+4xy+5y^2, with x and y nonnegativequadratic form35.9 %
A106932Primes of the form x^2 + xy + 17y^2, with x and y nonnegativequadratic form29.5 %
A106934Primes of the form 3x^2+2xy+6y^2, with x and y nonnegativequadratic form38.1 %
A106937Primes of the form 2x^2+2xy+9y^2, with x and y nonnegativequadratic form38.2 %
A106939Primes of the form 4x^2+3xy+5y^2, with x and y nonnegativequadratic form43.4 %
A106942Primes of the form 3x^2+xy+6y^2, with x and y nonnegativequadratic form42.2 %
A106945Primes of the form 2x^2+xy+9y^2, with x and y nonnegativequadratic form42.3 %
A106949Primes of the form 2x^2 + 9y^2quadratic form39.7 %
A106950Primes of the form x^2 + 18y^2quadratic form39.6 %
A106951Primes of the form 3x^2+3xy+7y^2, with x and y nonnegativequadratic form44.5 %
A106953Primes of the form 4x^2+2xy+5y^2, with x and y nonnegativequadratic form38.6 %
A106956Primes of the form 4x^2+xy+5y^2, with x and y nonnegativequadratic form40.0 %
A106959Primes of the form 2x^2+xy+10y^2, with x and y nonnegativequadratic form39.8 %
A106963Primes of the form 4x^2 + 5y^2quadratic form41.6 %
A106964Primes of the form 3x^2+2xy+7y^2, with x and y nonnegativequadratic form43.0 %
A106966Primes of the form 3x^2+xy+7y^2, with x and y nonnegativequadratic form37.3 %
A106969Primes of the form x^2+xy+21y^2, with x and y nonnegativequadratic form37.2 %
A106971Primes of the form 5x^2+4xy+5y^2, with x and y nonnegativequadratic form48.3 %
A106974Primes of the form 2x^2+2xy+11y^2, with x and y nonnegativequadratic form43.0 %
A106975Primes of the form 4x^2+3xy+6y^2, with x and y nonnegativequadratic form48.9 %
A106978Primes of the form 3x^2+3xy+8y^2, with x and y nonnegativequadratic form48.9 %
A106980Primes of the form 2x^2+xy+11y^2, with x and y nonnegativequadratic form47.9 %
A106984Primes of the form 2x^2 + 11y^2quadratic form35.2 %
A106985Primes of the form 5x^2+3xy+5y^2, with x and y nonnegativequadratic form38.7 %
A106988Primes of the form x^2+xy+23y^2, with x and y nonnegativequadratic form33.3 %
A106990Primes of the form 5x^2+5xy+6y^2, with x and y nonnegativequadratic form50.2 %
A106992Primes of the form 4x^2+xy+6y^2, with x and y nonnegativequadratic form47.9 %
A106995Primes of the form 3x^2+xy+8y^2, with x and y nonnegativequadratic form48.0 %
A106998Primes of the form 2x^2+xy+12y^2, with x and y nonnegativequadratic form47.8 %
A107002Primes of the form 5x^2+2xy+5y^2, with x and y nonnegativequadratic form49.7 %
A107003Primes of the form 24*k + 5primes44.9 %
A107005Primes of the form 4x^2+4xy+7y^2, with x and y nonnegativequadratic form46.3 %
A107006Primes of the form 4x^2-4xy+7y^2, with x and y nonnegativequadratic form44.4 %
A107007Primes of the form 3*x^2+8*y^2quadratic form44.3 %
A107008Primes of the form x^2 + 24*y^2quadratic form44.4 %
A107009Primes of the form 5x^2+xy+5y^2, with x and y nonnegativequadratic form46.4 %
A107012Primes of the form x^2+xy+25y^2, with x and y nonnegativequadratic form42.1 %
A107071Numbers k such that 1019*k + 1021 is primeprime values24.4 %
A107072Numbers k such that 1021*k + 1019 is primeprime values24.7 %
A107132Primes of the form 2x^2 + 13y^2quadratic form43.0 %
A107133Primes of the form 4x^2 + 7y^2quadratic form30.4 %
A107134Primes of the form x^2+28y^2quadratic form30.4 %
A107135Primes of the form 5x^2 + 6y^2quadratic form48.1 %
A107136Primes of the form 3x^2 + 10y^2quadratic form47.5 %
A107137Primes of the form 2x^2 + 15y^2quadratic form47.3 %
A107138Primes of the form 3x^2 + 11y^2quadratic form46.4 %
A107139Primes of the form 2x^2 + 17y^2quadratic form37.3 %
A107140Primes of the form 5x^2 + 7y^2quadratic form41.5 %
A107141Primes of the form 4x^2 + 9y^2quadratic form43.9 %
A107142Primes of the form x^2 + 36y^2quadratic form44.2 %
A107143Primes of the form 2x^2 + 19y^2quadratic form42.3 %
A107144Primes of the form 5x^2 + 8y^2quadratic form42.3 %
A107145Primes of the form x^2 + 40y^2quadratic form41.9 %
A107146Primes of the form 6x^2 + 7y^2quadratic form40.5 %
A107147Primes of the form 3x^2 + 14y^2quadratic form40.7 %
A107148Primes of the form 2x^2 + 21y^2quadratic form42.0 %
A107149Primes of the form 4x^2 + 11y^2quadratic form42.8 %
A107150Primes of the form x^2 + 44y^2quadratic form42.8 %
A107151Primes of the form 5x^2 + 9y^2quadratic form47.8 %
A107152Primes of the form x^2 + 45y^2quadratic form47.5 %
A107153Primes of the form 2x^2 + 23y^2quadratic form36.9 %
A107155Primes of the form x^2 + 49y^2quadratic form35.6 %
A107156Primes of the form 2x^2 + 25y^2quadratic form44.7 %
A107157Primes of the form x^2 + 50y^2quadratic form44.7 %
A107158Primes of the form 3x^2 + 17y^2quadratic form45.2 %
A107159Primes of the form 4x^2 + 13y^2quadratic form40.0 %
A107160Primes of the form x^2 + 52y^2quadratic form40.0 %
A107161Primes of the form 2x^2 + 27y^2quadratic form46.7 %
A107162Primes of the form x^2 + 54y^2quadratic form46.3 %
A107163Primes of the form 7x^2 + 8y^2quadratic form40.5 %
A107164Primes of the form x^2 + 56y^2quadratic form40.7 %
A107165Primes of the form 3x^2 + 19y^2quadratic form45.6 %
A107166Primes of the form 2x^2 + 29y^2quadratic form34.4 %
A107167Primes of the form 5x^2 + 12y^2quadratic form48.3 %
A107168Primes of the form 4x^2 + 15y^2quadratic form47.5 %
A107169Primes of the form 3x^2 + 20y^2quadratic form48.4 %
A107170Primes of the form 2x^2 + 31y^2quadratic form42.4 %
A107171Primes of the form 5x^2 + 13y^2quadratic form48.0 %
A107172Primes of the form 6x^2 + 11y^2quadratic form50.2 %
A107173Primes of the form 3x^2 + 22y^2quadratic form50.4 %
A107174Primes of the form 2x^2 + 33y^2quadratic form50.5 %
A107175Primes of the form 4x^2 + 17y^2quadratic form41.5 %
A107176Primes of the form x^2 + 68y^2quadratic form41.8 %
A107177Primes of the form 3x^2+23y^2quadratic form47.4 %
A107178Primes of the form 7x^2 + 10y^2quadratic form37.7 %
A107179Primes of the form 5x^2 + 14y^2quadratic form39.8 %
A107180Primes of the form 2x^2 + 35y^2quadratic form39.8 %
A107181Primes of the form 8x^2 + 9y^2quadratic form44.5 %
A107182Primes of the form 2x^2 + 37y^2quadratic form44.9 %
A107183Primes of the form 3x^2 + 25y^2quadratic form50.0 %
A107184Primes of the form x^2 + 75y^2quadratic form50.0 %
A107185Primes of the form 4x^2 + 19y^2quadratic form42.4 %
A107186Primes of the form x^2 + 76y^2quadratic form42.5 %
A107187Primes of the form 7x^2 + 11y^2quadratic form42.4 %
A107188Primes of the form 6x^2 + 13y^2quadratic form46.0 %
A107189Primes of the form 3x^2 + 26y^2quadratic form45.4 %
A107190Primes of the form 2x^2 + 39y^2quadratic form46.0 %
A107191Primes of the form 5x^2 + 16y^2quadratic form46.6 %
A107192Primes of the form x^2 + 80*y^2quadratic form46.8 %
A107193Primes of the form x^2 + 81y^2quadratic form46.9 %
A107194Primes of the form 2x^2 + 41y^2quadratic form37.9 %
A107195Primes of the form 7x^2 + 12y^2quadratic form45.8 %
A107196Primes of the form 4x^2 + 21y^2quadratic form46.2 %
A107197Primes of the form 3x^2 + 28y^2quadratic form46.0 %
A107198Primes of the form x^2 + 84y^2quadratic form46.2 %
A107199Primes of the form 5x^2 + 17y^2quadratic form40.6 %
A107200Primes of the form 2x^2 + 43y^2quadratic form45.1 %
A107201Primes of the form 8x^2 + 11y^2quadratic form40.2 %
A107202Primes of the form x^2 + 88y^2quadratic form40.1 %
A107203Primes of the form 9x^2 + 10y^2quadratic form52.3 %
A107204Primes of the form 5x^2 + 18y^2quadratic form52.0 %
A107205Primes of the form 2x^2 + 45y^2quadratic form51.8 %
A107206Primes of the form x^2 + 90y^2quadratic form52.0 %
A107207Primes of the form 7x^2 + 13y^2quadratic form40.0 %
A107208Primes of the form 4x^2 + 23y^2quadratic form40.1 %
A107209Primes of the form x^2 + 92y^2quadratic form40.0 %
A107210Primes of the form 3x^2 + 31y^2quadratic form42.8 %
A107211Primes of the form 2x^2 + 47y^2quadratic form42.4 %
A107212Primes of the form 3x^2 + 32y^2quadratic form48.7 %
A107213Primes of the form x^2 + 96y^2quadratic form48.5 %
A107214Primes of the form 2x^2 + 49y^2quadratic form40.4 %
A107215Primes of the form x^2 + 98y^2quadratic form40.7 %
A107216Primes of the form 9x^2 + 11y^2quadratic form48.3 %
A107217Primes of the form x^2 + 99y^2quadratic form48.2 %
A107218Primes of the form 4x^2 + 25y^2quadratic form41.7 %
A107219Primes of the form x^2 + 100y^2quadratic form41.6 %
A107288Primes whose digit sum is a squareprimes46.6 %
A107301Numbers k such that 10007*k + 99991 is primeprime values25.2 %
A107302Numbers k such that 99991*k + 10007 is primeprime values25.9 %
A107303Numbers k such that (3*k - 5) is primeprime values16.3 %
A107304Numbers k such that 5k - 7 is primeprime values20.3 %
A107305Numbers k such that 11*k - 13 is primeprime values22.4 %
A107306Numbers k such that (17*k - 19) is primeprime values23.2 %
A107308Numbers k such that (29*k - 31) is primeprime values23.9 %
A107366Numbers k such that 101*k + 103 is primeprime values24.3 %
A107369Numbers n such that 103*n + 101 is primeprime values23.9 %
A107371Numbers k such that 101*k - 103 is primeprime values24.0 %
A107372Numbers n such that 103*n - 101 is primeprime values24.0 %
A107400Numbers k such that 107*k + 109 is primeprime values23.8 %
A107405Numbers n such that 109*n + 107 is primeprime values24.3 %
A107406Numbers n such that 107*n - 109 is primeprime values24.1 %
A107407Numbers n such that 109*n - 107 is primeprime values24.3 %
A107665Numbers with semiprime digits (digits 4, 6, 9 only)digit rule16.2 %
A107666Primes having only {4, 6, 9} as digitsprimes40.4 %
A107715Primes having only {0,1,2,3} as digitsprimes28.9 %
A107960Numbers n such that 11*n - 1 is primeprime values22.6 %
A107992Numbers n such that 11*n - 3 is primeprime values16.1 %
A107994Numbers n such that 11*n - 2 is primeprime values32.7 %
A108027Numbers k such that 137*k + 139 is primeprime values24.2 %
A108028Numbers k such that 139*k + 137 is primeprime values24.3 %
A108029Numbers k such that 149*k + 151 is primeprime values24.2 %
A108030Numbers k such that 151*k + 149 is primeprime values24.0 %
A108058Numbers k such that 179*k + 181 is primeprime values24.3 %
A108059Numbers k such that 181*k + 179 is primeprime values24.2 %
A108060Numbers k such that 191*k + 193 is primeprime values24.8 %
A108061Numbers k such that 193*k + 191 is primeprime values24.4 %
A108099a(n) = 8*n^2 + 8*n + 4polynomial100.0 %
A108100a(n) = (2*n-1)^2 + (2*n+1)^2polynomial100.0 %
A108181Semiprimes of the form 4n + 1multiplicative26.2 %
A108187Numbers n such that 11*n - 5 is primeprime values20.8 %
A108195a(n) = n^2 + 5*n - 1polynomial100.0 %
A108211a(n) = 16*n^2 + 1polynomial100.0 %
A108232Numbers n such that 11*n - 7 is primeprime values21.6 %
A108233Numbers n such that 11*n + 5 is primeprime values20.4 %
A108341Numbers n such that 997*n - 1009 is primeprime values24.8 %
A108342Numbers n such that 1009*n - 997 is primeprime values24.6 %
A108386Primes p such that p's set of distinct digits is {1,3,7,9}primes30.6 %
A108584Numbers k such that 10*k - 97 is primeprime values21.8 %
A108588Numbers k such that 10*k + 97 is primeprime values20.7 %
A108594Numbers k such that 10*k + 101 is primeprime values22.1 %
A108595Numbers k such that 10*k + 103 is primeprime values21.8 %
A108596Numbers k such that 911*k - 7 is primeprime values23.9 %
A108597Numbers n such that 911*n - 11 is primeprime values24.3 %
A108598a(n) = floor(n*((5+sqrt(5))/4))Beatty13.0 %
A108601Numbers n such that 7*n - 911 is primeprime values21.9 %
A108724Numbers n such that 11*n + 17 is primeprime values22.4 %
A108725Numbers n such that 11*n + 19 is primeprime values22.6 %
A108726Numbers n such that 11*n + 29 is primeprime values23.4 %
A108727Numbers n such that 11*n + 31 is primeprime values22.9 %
A108751Numbers k such that 11*k - 911 is primeprime values22.9 %
A108757Numbers k such that 1000*k + 911 is primeprime values22.5 %
A108762Numbers n such that 911*n + 13 is primeprime values24.4 %
A108769Numbers m such that m^2 + (m+1)^2 is a semiprimemultiplicative15.8 %
A108854Numbers k such that 10*k - 127 is primeprime values21.0 %
A108855Numbers n such that 10*n + 127 is primeprime values22.0 %
A108856Numbers k such that 10*k - 131 is primeprime values21.8 %
A108857Numbers n such that 10*n + 131 is primeprime values21.2 %
A108874Numbers k such that 41*k + 43 is primeprime values23.8 %
A108899Numbers k such that 11*k + 2357 is primeprime values22.7 %
A108900Numbers k such that 2357*k + 11 is primeprime values24.5 %
A108901Numbers n such that 2357*n + 23 is primeprime values24.8 %
A108902Numbers k such that 23*k + 2357 is primeprime values23.6 %
A108928a(n) = 8*n^2 - 3polynomial100.0 %
A108935Numbers k such that 7*k + 911 is primeprime values22.2 %
A108936Numbers n such that 11*n + 911 is primeprime values22.7 %
A108937Numbers k such that 911*k + 11 is primeprime values24.6 %
A108938Numbers k such that 911*k + 7 is primeprime values23.6 %
A108969Numbers n such that 43*n + 41 is primeprime values23.9 %
A108976Numbers k such that 17*k + 19 is primeprime values23.2 %
A108977Numbers n such that 19*n + 17 is primeprime values23.6 %
A108978Numbers k such that 29*k + 31 is primeprime values23.1 %
A108979Numbers k such that 31*k + 29 is primeprime values23.1 %
A109303Numbers k with at least one duplicate base-10 digit (A107846(k) > 0)digit rule10.7 %
A109373Semiprimes of the form semiprime + 1multiplicative30.3 %
A109603Numbers n such that 43*n - 41 is primeprime values24.2 %
A109604Numbers n such that 41*n - 43 is primeprime values23.6 %
A109605Numbers n such that 100000n + 91111 is primeprime values23.8 %
A109611Chen primes: primes p such that p + 2 is either a prime or a semiprimeprimes34.5 %
A109953Primes p such that p^2+2 is a semiprimeprimes41.2 %
A110451a(n) = n*(4*n^2 + 2*n + 1)polynomial100.0 %
A110801Numbers k such that 12k + 1 is primeprime values18.3 %
A110831a(n) = 3*n^2 + 27*n + 1polynomial100.0 %
A110913Numbers n such that 23*n^2 - 49 is primeprime values20.7 %
A110959Numbers k such that 23*k^2 + 1 is primeprime values18.8 %
A110960Numbers n such that 23*n^2 + 4 is primeprime values28.3 %
A110961Numbers k such that 23*k^2 + 9 is primeprime values17.6 %
A110964Numbers k such that 23*k^2 + 16 is primeprime values28.3 %
A110965Numbers k such that 23*k^2 + 25 is primeprime values19.2 %
A110966Numbers k such that 23*k^2 + 36 is primeprime values27.7 %
A110967Numbers k such that 23*k^2 + 49 is primeprime values19.6 %
A110974Numbers n such that 23*n^2 - 1 is primeprime values23.1 %
A110994Numbers n such that 23*n^2 - 4 is primeprime values32.2 %
A110998Numbers n such that 23*n^2 - 9 is primeprime values22.6 %
A110999Numbers n such that 23*n^2 - 16 is primeprime values32.0 %
A111001Numbers n such that 23*n^2 - 25 is primeprime values23.4 %
A111040Numbers n such that 2*n^2 + 9 is primeprime values17.9 %
A111041Numbers m such that 2*m^2 + 25 is primeprime values19.8 %
A111046Difference between squares of twin prime pairsprimes32.3 %
A111051Numbers m such that 3*m^2 + 1 is primeprime values21.5 %
A111052Numbers m such that 3*m^2 + 4 is primeprime values30.8 %
A111068Numbers k such that 3*k^2 + 16 is primeprime values30.8 %
A111069Numbers k such that 3*k^2 + 25 is primeprime values21.9 %
A111082Numbers n such that 3*n^2 + 49 is primeprime values18.8 %
A111083Numbers k such that 3*k^2 + 64 is primeprime values30.7 %
A111094Numbers k such that 18*k + 1 is primeprime values18.2 %
A111144a(n) = n*(n+13)*(n+14)/6polynomial100.0 %
A111147Numbers k such that 5*k^2 + 1 is primeprime values20.7 %
A111148Numbers k such that 5*k^2 + 4 is primeprime values30.2 %
A111149Numbers k such that 5*k^2 + 9 is primeprime values19.8 %
A111174Numbers k such that 24*k + 1 is primeprime values18.6 %
A111175Numbers k such that 30*k + 1 is primeprime values16.8 %
A111199Numbers k such that 4k + 9 is primeprime values16.3 %
A111215Numbers k such that 4k + 5 is primeprime values20.7 %
A111223Numbers n such that 5*n + 2 is primeprime values30.2 %
A111224Numbers n such that 5*n + 7 is primeprime values20.2 %
A111225Numbers n such that 5*n + 8 is primeprime values30.6 %
A111226Numbers k such that 5*k + 12 is primeprime values25.1 %
A111230Numbers k such that 5*k + 14 is primeprime values29.1 %
A111249Numbers k such that 7*k + 8 is primeprime values30.2 %
A111250Numbers n such that 7*n + 10 is primeprime values29.4 %
A111251Numbers k such that 3*k^2 + 3*k + 1 is primeprime values21.1 %
A111292Numbers n such that 6*n^2 + 6*n + 1 is primeprime values19.7 %
A111294Numbers n such that 23*n + 2 is primeprime values31.4 %
A111312Numbers n such that 11*n + 2 is primeprime values30.7 %
A111367Numbers k such that 7*k + 5 is primeprime values20.0 %
A111369Numbers k such that 13*k + 11 is primeprime values22.6 %
A111396a(n) = n*(n+7)*(n+8)/6polynomial100.0 %
A111455Numbers k such that 101*k + 97 is primeprime values24.1 %
A111488Primes having only {0, 1, 3, 6} as digitsprimes32.1 %
A111501Numbers k such that k^3 - k^2 + 1 is primeprime values22.9 %
A111592Admirable numbers. A number n is admirable if there exists a proper divisor d' of n such that sigma(n)-2d'=2n, where sigma(n) is the sum of all divisors of ndivisor functions24.8 %
A112087a(n) = 4*(n^2 - n + 1)polynomial100.0 %
A112391Primes p such that 23*p + 2 is also primeprimes48.2 %
A112771Semiprimes of the form 6n + 1multiplicative33.5 %
A112772Semiprimes of the form 6n+2multiplicative35.3 %
A112774Semiprimes of the form 6n+4multiplicative35.2 %
A112775Numbers k such that 6k+1 is semiprimemultiplicative14.2 %
A112776Numbers k such that 6k+5 is semiprimemultiplicative13.3 %
A112777Numbers k such that 2*k^2 + 1 is a semiprimemultiplicative17.9 %
A112886Positive integers that have no triangular divisors > 1divisor functions2.3 %
A113115Primes p such that 17*p + 2 is also primeprimes47.9 %
A113151Primes p such that 19*p + 2 is also primeprimes47.9 %
A113169Primes p such that 13*p + 2 is also primeprimes47.4 %
A113487Numbers k such that 17*k + 2 is primeprime values33.4 %
A113488Numbers k such that 19*k + 2 is primeprime values32.9 %
A113502A number n is included if at least one of its divisors > 1 is a triangular number (i.e., is of the form m(m+1)/2, m >= 2)divisor functions14.5 %
A113510Numbers k such that 29*k + 2 is primeprime values33.5 %
A113536Numbers k such that k^2 + 13 is primeprime values22.9 %
A113801Numbers that are congruent to {1, 13} mod 14residue class26.8 %
A113802Numbers that are congruent to {2, 12} mod 14residue class19.7 %
A113803Numbers that are congruent to {3, 11} mod 14residue class30.1 %
A113805Numbers that are congruent to {5, 9} mod 14residue class29.2 %
A113806Numbers that are congruent to {6, 8} mod 14residue class18.0 %
A114211a(n) = (5*n^3+12*n^2+n+6)/6polynomial100.0 %
A114269Numbers k such that k^2 + 6 is primeprime values35.3 %
A114270Numbers k such that k^2 + 7 is primeprime values19.2 %
A114271Numbers k such that k^2 + 8 is primeprime values28.9 %
A114272Numbers k such that k^2 + 9 is primeprime values23.3 %
A114273Numbers k such that k^2 + 10 is primeprime values32.7 %
A114274Numbers k such that k^2 + 11 is primeprime values23.3 %
A114275Numbers k such that k^2 + 12 is primeprime values30.1 %
A114364a(n) = n*(n+1)^2polynomial100.0 %
A114444a(n) = 16*n*(n+2)polynomial100.0 %
A114948a(n) = n^2 + 10polynomial100.0 %
A114949a(n) = n^2 + 6polynomial100.0 %
A114962a(n) = n^2 + 14polynomial100.0 %
A114963a(n) = n^2 + 22polynomial100.0 %
A114964a(n) = n^2 + 30polynomial100.0 %
A114965a(n) = n^2 + 34polynomial100.0 %
A115067a(n) = (3*n^2 - n - 2)/2polynomial100.0 %
A115519a(n) = n*(1+3*n+6*n^2)/2polynomial100.0 %
A116668a(n) = (5*n^2 + n + 2)/2polynomial100.0 %
A117047Primes of the form 60*k + 11primes52.7 %
A117048Prime numbers that are expressible as the sum of two positive triangular numbersprimes34.5 %
A117049Primes of the form 22*(n^2)+1primes100.0 %
A117560a(n) = n*(n^2 - 1)/2 - 1polynomial100.0 %
A117619a(n) = n^2 + 7polynomial100.0 %
A117642a(n) = 3*n^3polynomial100.0 %
A117804Natural position of n in the string 12345678910111213...digit rule10.7 %
A117950a(n) = n^2 + 3polynomial100.0 %
A117951a(n) = n^2 + 5polynomial100.0 %
A118057a(n) = 8*n^2 - 4*n - 3polynomial100.0 %
A118058a(n) = 49n^2 - 28n - 20polynomial100.0 %
A118059a(n) = 288*n^2 - 168*n - 119polynomial100.0 %
A118060a(n) = 1681*n^2 - 984*n - 696polynomial100.0 %
A118061a(n) = 9800*n^2-5740*n-4059polynomial100.0 %
A118134Primes p such that 4p is the sum of two consecutive primesprimes46.7 %
A118363Factorial base Niven (or Harshad) numbers: numbers that are divisible by the sum of their factorial base digitsdigit rule22.4 %
A118465a(n) = 8*n^3 + npolynomial100.0 %
A118882Numbers which are the sum of two squares in two or more different waysquadratic form19.9 %
A118886Numbers expressible as x^2 + x*y + y^2, 0 <= x <= y, in 2 or more waysquadratic form29.3 %
A118922Primes for which the weight as defined in A117078 is 9 and the gap as defined in A001223 is 8primes57.0 %
A118950Numbers containing at least one prime digitdigit rule10.2 %
A118951Numbers containing at least one composite digitdigit rule9.9 %
A118954Numbers that cannot be written as 2^k + primeprimes8.6 %
A118955Numbers of the form 2^k + primeprimes32.2 %
A119409Numbers k such that 235*k + 1 is primeprime values23.1 %
A119412a(n) = n*(n+11)polynomial100.0 %
A119449Primes with even digit sumprimes28.4 %
A119536a(n) = 3*n^3 + 3*npolynomial100.0 %
A119735Numbers n such that every digit occurs at least once in n^3digit rule20.2 %
A120071a(n) = n*(n+20)polynomial100.0 %
A120330Primes not congruent to +- 1, 3, or 4 (mod 13)primes30.8 %
A120344Numbers k such that 23*k + 1 is a primeprime values23.1 %
A120345Numbers n such that 2357*n + 1 is primeprime values25.2 %
A120944Composite squarefree numbersmultiplicative11.9 %
A121022Even numbers containing a 2 in their decimal representationdigit rule11.5 %
A121030Multiples of 10 containing a 10 in their decimal representationdigit rule24.3 %
A121032Multiples of 12 containing a 12 in their decimal representationdigit rule19.6 %
A121068Numbers k such that 8*k^2 + 7 is primeprime values24.4 %
A121250Numbers n such that n^2 + 14 is primeprime values34.2 %
A121283a(n) = floor(n*Pi*e)Beatty23.7 %
A121495Numbers k such that k and k+1 are composite and squarefreemultiplicative16.2 %
A121539Numbers whose binary expansion ends in an even number of 1'sbinary rule12.0 %
A121817Numbers m such that 23 + 36*m*(m+1) is primeprime values23.3 %
A121982Numbers k such that k^2 + 15 is primeprime values18.3 %
A122062Numbers k such that k^2 + 16 is primeprime values33.3 %
A122094Prime divisors of Mersenne numbers. Primes p such that the multiplicative order of 2 modulo p is primeprimes48.9 %
A122114Primes of the form 2n^2 + 26n + 1primes100.0 %
A122430Primes of the form 1+2*n+3*n^2primes100.0 %
A122482Primes p such that 1 + 4p + 12p^2 is primeprimes49.0 %
A122488Numbers k such that 1 + 2k + 3k^2 is semiprimemultiplicative17.7 %
A122535Smallest prime of a triple of successive primes, where the middle one is the arithmetic mean of the other twoprimes46.5 %
A122562a(n) = n^3 + 114 * npolynomial100.0 %
A122870Primes congruent to 3 or 7 mod 20primes37.2 %
A123017Semiprimes k such that k+3 is also a semiprimemultiplicative23.4 %
A123193Natural numbers with number of divisors equal to a Fibonacci numberdivisor functions14.0 %
A123239Primes that do not divide 3^k - 2 for any kprimes29.9 %
A124127Numbers k such that 17k + 1 is primeprime values23.1 %
A124198Numbers k such that 21*k + 1 is primeprime values18.6 %
A124204Numbers k such that 20*k + 1 is primeprime values21.3 %
A124268Primes indexed by 3-almost primesprimes33.2 %
A1242693-almost primes indexed by primesmultiplicative33.6 %
A124282Primes indexed by 4-almost primesprimes35.2 %
A1242834-almost primes indexed by primesmultiplicative33.7 %
A124594Primes p such that q-p = 26, where q is the next prime after pprimes56.8 %
A124595Primes p such that q-p = 28, where q is the next prime after pprimes56.0 %
A124596Primes p such that q-p = 30, where q is the next prime after pprimes47.3 %
A124826Primes congruent to 1 mod 21primes49.9 %
A124940Numbers k such that k and k+3 are 3-almost primesmultiplicative23.0 %
A124941Numbers k such that k and k+4 are 4-almost primesmultiplicative26.2 %
A125022Numbers with a unique partition as the sum of 2 squares x^2 + y^2quadratic form18.1 %
A125200a(n) = n*(4*n^2 + n - 1)/2polynomial100.0 %
A125201a(n) = 8*n^2 - 7*n + 1polynomial100.0 %
A125272Primes p such that 3p - 2 and 3p + 2 are also primesprimes56.7 %
A125308Primes having only {0, 1, 3, 8} as digitsprimes32.3 %
A125830Primes for which the level is equal to 1 in A117563primes49.8 %
A126148Primes p such that pq+p+q is prime, where q is the next prime after pprimes42.1 %
A126264a(n) = 5*n^2 + 3*npolynomial100.0 %
A126332Numbers k such that 10k + 13 is primeprime values20.8 %
A126335a(n) = n*(4*n^2+5*n-3)/2polynomial100.0 %
A126721Primes p such that q-p = 40, where q is the next prime after pprimes60.4 %
A126784Primes p such that q-p = 32, where q is the next prime after pprimes60.1 %
A126785Numbers k such that 10*k + 11 is primeprime values21.0 %
A126960Primes p such that (3p)^2 + 2 is primeprimes38.5 %
A126964a(n) = 2*n*(6*n-1)polynomial100.0 %
A127316a(n) = 2*n^2 - 4*n + 73polynomial100.0 %
A127333Numbers that are the sum of 6 consecutive primesprimes34.3 %
A127334Numbers that are the sum of 7 consecutive primesprimes44.2 %
A127336Numbers that are the sum of 9 consecutive primesprimes45.9 %
A127337Numbers that are the sum of 10 consecutive primesprimes37.6 %
A127338Numbers that are the sum of 11 consecutive primesprimes47.4 %
A127339Numbers that are the sum of 12 consecutive primesprimes39.0 %
A127340Primes that are the sum of 11 consecutive primesprimes56.2 %
A127341Primes that can be written as the sum of 13 consecutive primesprimes57.6 %
A127435Primes p such that (p-1)^2 + 1 is primeprimes42.8 %
A127575Numbers n such that 16n+15 is primeprime values16.2 %
A127576Primes of the form 16n+15primes38.3 %
A127578Primes congruent to 31 mod 32primes43.2 %
A127579Primes of the form 64n+63primes47.8 %
A127580Numbers k such that 64k+63 is primeprime values17.6 %
A127589Primes of the form 16k + 5primes38.5 %
A127590Numbers n such that 16n+5 is primeprime values21.2 %
A127591Numbers k such that 64k+21 is primeprime values17.4 %
A127592Primes of the form 64k+21primes47.7 %
A127593Primes of the form 256 k + 85primes58.3 %
A127594Numbers k such that 256 k + 85 is primeprime values22.3 %
A127736a(n) = n*(n^2 + 2*n - 1)/2polynomial100.0 %
A127989a(n) = 2*n^3 - 2*n + 9polynomial100.0 %
A128464Numbers that are congruent to {11, 17, 29} mod 30residue class30.6 %
A128829Numbers k such that 6*k^2 + 17 is primeprime values17.6 %
A128928Smallest member p of a triple of primes (p,p+8,p+20)primes60.2 %
A129484Primes of the form 17k + 1primes44.5 %
A129805Primes congruent to +-1 mod 18primes32.4 %
A129806Primes congruent to +-5 mod 18primes34.4 %
A129807Primes congruent to +-7 mod 18primes33.7 %
A129845Numbers n such that n and 2n share at least one digitdigit rule9.8 %
A130091Numbers having in their canonical prime factorization mutually distinct exponentsmultiplicative17.0 %
A130861a(n) = (n-1)*(2*n+5)polynomial100.0 %
A130862a(n) = (n-1)*(n+2)*(2*n+11)/2polynomial100.0 %
A130877Numbers that are congruent to {0, 5} mod 9residue class24.2 %
A130883a(n) = 2*n^2 - n + 1polynomial100.0 %
A130884a(n) = 3n^3 + 2n^2 + n + 1polynomial100.0 %
A130885a(n) = 3n^3 - 2n^2 + n - 1polynomial100.0 %
A131210Numbers k such that 24k - 1 is primeprime values18.5 %
A131229Numbers congruent to {1,7} mod 10residue class23.8 %
A131323Odd numbers whose binary expansion ends in an even number of 1'sbinary rule25.6 %
A131464a(n) = 4*n^3 - 3*n^2 + 2*n - 1polynomial100.0 %
A131645Beastly primes (version 2): primes containing 666 as a substringprimes32.6 %
A131835Numbers starting with 1digit rule8.7 %
A131874a(n) = (7*n^2 + 15*n + 2) / 2polynomial100.0 %
A131878a(n) = 7*n^2 + 14*n + 1polynomial100.0 %
A131895a(n) = (n + 2)*(5*n + 1)/2polynomial100.0 %
A132112a(n) = n*(n+1)*(11*n+1)/6polynomial100.0 %
A132124a(n) = n*(n+1)*(8*n + 1)/6polynomial100.0 %
A132127a(n) = (n^3 + 3*n - 2)/2polynomial100.0 %
A132190Numbers n such that 7*n^2 + 1 is primeprime values19.2 %
A132208a(n) = 15*n*(n+1) + 11polynomial100.0 %
A132230Primes congruent to 1 (mod 30)primes48.3 %
A132231Primes congruent to 7 (mod 30)primes48.5 %
A132232Primes congruent to 11 (mod 30)primes48.5 %
A132233Primes congruent to 13 (mod 30)primes48.3 %
A132234Primes congruent to 19 (mod 30)primes48.4 %
A132235Primes congruent to 23 (mod 30)primes48.4 %
A132236Primes congruent to 29 (mod 30)primes48.7 %
A132237Primes congruent to {7, 23} mod 30primes38.0 %
A132238Primes congruent to {11, 13} mod 30primes31.0 %
A132239Primes congruent to {17, 19} mod 30primes32.9 %
A132240Primes congruent to {1, 29} mod 30primes35.7 %
A132359Numbers divisible by the square of their last decimal digitdigit rule22.0 %
A132398Numbers n such that 11*n^2 + 1 is primeprime values23.9 %
A132754a(n) = n*(n + 23)/2polynomial100.0 %
A132755a(n) = n*(n + 25)/2polynomial100.0 %
A132756a(n) = n*(n + 27)/2polynomial100.0 %
A132757a(n) = n*(n+29)/2polynomial100.0 %
A132758a(n) = n*(n + 31)/2polynomial100.0 %
A132759a(n) = n*(n+13)polynomial100.0 %
A132760a(n) = n*(n+15)polynomial100.0 %
A132761a(n) = n*(n+17)polynomial100.0 %
A132762a(n) = n*(n + 19)polynomial100.0 %
A132763a(n) = n*(n+21)polynomial100.0 %
A132764a(n) = n*(n+22)polynomial100.0 %
A132765a(n) = n*(n + 23)polynomial100.0 %
A132766a(n) = n*(n+24)polynomial100.0 %
A132767a(n) = n*(n + 25)polynomial100.0 %
A132768a(n) = n*(n + 26)polynomial100.0 %
A132769a(n) = n*(n + 27)polynomial100.0 %
A132770a(n) = n*(n + 28)polynomial100.0 %
A132771a(n) = n*(n + 29)polynomial100.0 %
A132772a(n) = n*(n + 30)polynomial100.0 %
A132773a(n) = n*(n + 31)polynomial100.0 %
A133157Numbers k such that k^2 + k - 41 is primeprime values27.0 %
A133496a(n) = (29*n)^2polynomial100.0 %
A133694a(n) = (3*n^2 + 3*n - 4)/2polynomial100.0 %
A133765Primes that contain the digit 4 or the digit 9primes24.8 %
A133783Primes containing only digits from set {1,2,3,4,5,6}primes28.5 %
A133869Numbers k such that 32*k + 1 is primeprime values24.0 %
A133870Primes of the form 32*n + 1primes43.2 %
A134027Nonnegative numbers that are palindromes in balanced ternary representationdigit rule93.8 %
A134116Primes p such that q-p = 34, where q is the next prime after pprimes60.1 %
A134117Primes p such that q-p = 36, where q is the next prime after pprimes51.6 %
A134118Primes p such that q - p = 38, where q is the next prime after pprimes61.9 %
A134120Primes p such that q-p = 42, where q is the next prime after pprimes53.2 %
A134121Primes p such that q-p = 44, where q is the next prime after pprimes64.0 %
A134122Primes p such that q-p = 46, where q is the next prime after pprimes65.4 %
A134123Primes p such that q-p = 48, where q is the next prime after pprimes56.6 %
A134124Primes p such that q-p = 50, where q is the next prime after pprimes65.2 %
A134153a(n) = 15*n^2 + 9*n + 1polynomial100.0 %
A134154a(n) = 15*n^2 - 9*n + 1polynomial100.0 %
A134333Numbers n whose number of prime factors (counted with multiplicity) is a prime factor of nmultiplicative17.3 %
A134334Numbers which are not divisible by the number of their prime factors (counted with multiplicity)multiplicative10.8 %
A134344Composite numbers such that the arithmetic mean of their prime factors (counted with multiplicity) is primemultiplicative30.3 %
A134376Numbers whose sum of prime factors (counted with multiplicity) is not primemultiplicative10.6 %
A134517Primes of the form 24*k - 1primes44.4 %
A134538a(n) = 5*n^2 - 1polynomial100.0 %
A134547a(n) = 5*n^2 + 20*n + 4polynomial100.0 %
A134582a(n) = (2*n)^2 - 4polynomial100.0 %
A134616Numbers such that the sum of squares of their prime factors (taken with multiplicity) is a primemultiplicative24.7 %
A134617Numbers such that the arithmetic mean of the squares of their prime factors (taken with multiplicity) is a primemultiplicative29.3 %
A134618Numbers such that the sum of cubes of their prime factors (taken with multiplicity) is a primemultiplicative28.3 %
A134619Numbers such that the arithmetic mean of the cubes of their prime factors (taken with multiplicity) is a primemultiplicative39.5 %
A134671Primes of the form 2m*691 - 1primes73.2 %
A134809Cyclops primesprimes20.3 %
A134934a(n) = (14*n+1)^2polynomial100.0 %
A135453a(n) = 12*n^2polynomial100.0 %
A135628Multiples of 28residue class9.6 %
A135631Multiples of 31residue class9.7 %
A135703a(n) = n*(7*n-2)polynomial100.0 %
A135706a(n) = n*(5*n-3)polynomial100.0 %
A135712a(n) = (4*n^3 + 11*n^2 + 9*n + 2)/2polynomial100.0 %
A135713a(n) = n*(n+1)*(4*n+1)/2polynomial100.0 %
A136016a(n) = 9*n^2-1polynomial100.0 %
A136017a(n) = 36n^2 - 1polynomial100.0 %
A136051Primes p such that 5*p-4 is also primeprimes45.6 %
A136072Primes of the form 7*p + 6 with p primeprimes50.8 %
A136260Primes which contain the digit 2 or the digit 3primes24.3 %
A136333Numbers containing only digits coprime to 10 in their decimal representationdigit rule17.5 %
A136392a(n) = 6*n^2 - 10*n + 5polynomial100.0 %
A136773n! never ends in this many 0's in base 13powers25.9 %
A137238Primes which contain the digit 1 or the digit 2primes24.1 %
A137270Primes p such that p^2 - 6 is also primeprimes44.9 %
A137487Numbers with 24 divisorsmultiplicative20.9 %
A137491Numbers with 28 divisorsmultiplicative25.5 %
A137493Numbers with 30 divisorsmultiplicative36.0 %
A137530Primes of the form 5k^2 + 1primes100.0 %
A137977Primes congruent to {0, 2, 4, 6, 8, 10} modulo 11primes28.5 %
A137978Primes congruent to {1, 3, 5, 7, 9} modulo 11primes28.2 %
A138218Numbers k such that 180k^2 + 1 is primeprime values20.7 %
A138220Numbers k such that 900*k^2 + 1 is primeprime values19.7 %
A138338Primes of the form n^2+8primes100.0 %
A138353Primes of the form k^2 + 9primes100.0 %
A138355Primes of the form k^2 + 10primes100.0 %
A138362Primes of the form k^2 + 11primes100.0 %
A138368Primes of the form k^2 + 12primes100.0 %
A138375Primes of the form k^2 + 13primes100.0 %
A138511Semiprimes where the larger prime factor is greater than the square of the smaller prime factor, short: semiprimes p*q, p^2 < qmultiplicative18.2 %
A138623Primes congruent to 5 mod 17primes44.4 %
A138625Primes congruent to 12 mod 17primes44.4 %
A138627Primes congruent to 10 mod 17primes44.3 %
A138629Primes of form 17*n+7primes44.4 %
A138631Primes of the form 17*k + 9primes44.5 %
A138633Primes of the form 17*k - 9primes44.6 %
A138638Primes of form 19*n-1primes45.0 %
A138640Primes of form 19*n-2primes45.0 %
A138642Primes of form 19*n-3primes45.1 %
A138918Numbers n such that 18n-1 is primeprime values18.8 %
A139098a(n) = 8*n^2polynomial100.0 %
A139271a(n) = 2*n*(4*n-3)polynomial100.0 %
A139272a(n) = n*(8*n-5)polynomial100.0 %
A139273a(n) = n*(8*n - 3)polynomial100.0 %
A139274a(n) = n*(8*n-1)polynomial100.0 %
A139275a(n) = n*(8*n+1)polynomial100.0 %
A139276a(n) = n*(8*n+3)polynomial100.0 %
A139277a(n) = n*(8*n+5)polynomial100.0 %
A139278a(n) = n*(8*n+7)polynomial100.0 %
A139483Numbers k such that 24*k + 7 is primeprime values18.0 %
A139487Numbers k such that 8k + 7 is primeprime values22.2 %
A139489Primes of the form x^2+101y^2quadratic form46.9 %
A139513Primes congruent to {1, 3, 7, 9} mod 20primes28.1 %
A139528Numbers k such that 24*k + 11 is primeprime values18.2 %
A139529Numbers k such that 24*k + 13 is primeprime values18.3 %
A139530Primes of the form 24*k + 13primes44.7 %
A139531Numbers k such that 24*k + 17 is primeprime values18.7 %
A139532Numbers k such that 24*k + 19 is primeprime values18.5 %
A139570a(n) = 2*n*(n+3)polynomial100.0 %
A139576a(n) = n*(2*n + 9)polynomial100.0 %
A139577a(n) = n*(2*n + 11)polynomial100.0 %
A139578a(n) = n*(2*n + 13)polynomial100.0 %
A139579a(n) = 2*n^2 + 15*npolynomial100.0 %
A139580a(n) = n*(2*n + 17)polynomial100.0 %
A139581a(n) = n*(2*n + 19)polynomial100.0 %
A139639Numbers n such that 168n+31 is primeprime values18.2 %
A139644Primes of the form x^2 + 105*y^2quadratic form49.4 %
A139645Primes of the form x^2 + 112*y^2quadratic form35.2 %
A139646Primes of the form x^2 + 130*y^2quadratic form43.5 %
A139647Primes of the form x^2 + 133*y^2quadratic form36.9 %
A139648Primes of the form x^2 + 165*y^2quadratic form53.6 %
A139649Primes of the form x^2 + 177*y^2quadratic form44.6 %
A139650Primes of the form x^2 + 190*y^2quadratic form42.9 %
A139651Primes of the form x^2 + 210*y^2quadratic form48.7 %
A139652Primes of the form x^2 + 232*y^2quadratic form39.1 %
A139653Primes of the form x^2 + 253*y^2quadratic form39.2 %
A139654Primes of the form x^2+273y^2quadratic form47.7 %
A139655Primes of the form x^2 + 280*y^2quadratic form43.7 %
A139656Primes of the form x^2 + 312*y^2quadratic form50.3 %
A139657Primes of the form x^2 + 330*y^2quadratic form53.9 %
A139658Primes of the form x^2 + 345*y^2quadratic form51.2 %
A139659Primes of the form x^2 + 357*y^2quadratic form44.8 %
A139660Primes of the form x^2 + 385*y^2quadratic form46.2 %
A139661Primes of the form x^2 + 408*y^2quadratic form47.4 %
A139662Primes of the form x^2 + 462*y^2quadratic form48.4 %
A139663Primes of the form x^2 + 520*y^2quadratic form47.9 %
A139664Primes of the form x^2 + 760*y^2quadratic form47.8 %
A139665Primes of the form x^2 + 840*y^2quadratic form53.5 %
A139666Primes of the form x^2 + 1320*y^2quadratic form58.6 %
A139667Primes of the form x^2 + 1365*y^2quadratic form55.6 %
A139668Primes of the form x^2 + 1848*y^2quadratic form53.0 %
A139757a(n) = (n+1)*(2n+1)^2polynomial100.0 %
A139841Primes of the form 2x^2 + 51y^2quadratic form42.7 %
A139842Primes of the form 3x^2 + 34y^2quadratic form42.7 %
A139843Primes of the form 6x^2 + 17y^2quadratic form42.7 %
A139845Primes of the form 3x^2 + 35y^2quadratic form50.6 %
A139846Primes of the form 5x^2 + 21y^2quadratic form49.8 %
A139848Primes of the form 7x^2 + 15y^2quadratic form48.5 %
A139852Primes of the form 7x^2 + 16y^2quadratic form35.3 %
A139854Primes of the form 3x^2 + 40y^2quadratic form52.4 %
A139856Primes of the form 5x^2 + 24y^2quadratic form52.9 %
A139857Primes of the form 8x^2 + 15y^2quadratic form52.4 %
A139861Primes of the form 2x^2 + 65y^2quadratic form43.5 %
A139862Primes of the form 5x^2 + 26y^2quadratic form43.9 %
A139863Primes of the form 10x^2 + 13y^2quadratic form43.3 %
A139865Primes of the form 7x^2 + 19y^2quadratic form36.6 %
A139868Primes of the form 3x^2 + 55y^2quadratic form54.3 %
A139869Primes of the form 5x^2 + 33y^2quadratic form54.3 %
A139872Primes of the form 11x^2 + 15y^2quadratic form53.7 %
A139874Primes of the form 3x^2 + 56y^2quadratic form45.8 %
A139876Primes of the form 7x^2+24y^2quadratic form45.8 %
A139877Primes of the form 8x^2+21y^2quadratic form46.7 %
A139882Primes of the form 3x^2+59y^2quadratic form44.7 %
A139884Primes of the form 2x^2+95y^2quadratic form43.1 %
A139885Primes of the form 5x^2+38y^2quadratic form43.4 %
A139886Primes of the form 10x^2 + 19y^2quadratic form43.0 %
A139887Primes of the form 2x^2+105y^2quadratic form49.9 %
A139888Primes of the form 3x^2+70y^2quadratic form48.7 %
A139889Primes of the form 5x^2+42y^2quadratic form48.8 %
A139890Primes of the form 6x^2+35y^2quadratic form50.7 %
A139891Primes of the form 7x^2+30y^2quadratic form50.0 %
A139892Primes of the form 10x^2+21y^2quadratic form50.6 %
A139893Primes of the form 14x^2+15y^2quadratic form49.0 %
A139895Primes of the form 8x^2+29y^2quadratic form39.7 %
A139897Primes of the form 3*x^2+80*y^2quadratic form52.2 %
A139899Primes of the form 5x^2+48y^2quadratic form52.4 %
A139904Primes of the form 2x^2+2xy+127y^2quadratic form39.5 %
A139905Primes of the form 11x^2+23y^2quadratic form39.1 %
A139908Primes of the form 3x^2+91y^2quadratic form47.6 %
A139910Primes of the form 7x^2+39y^2quadratic form47.5 %
A139911Primes of the form 13x^2+21y^2quadratic form47.6 %
A139915Primes of the form 5x^2+56y^2quadratic form44.4 %
A139916Primes of the form 7x^2+40y^2quadratic form43.2 %
A139917Primes of the form 8x^2+35y^2quadratic form43.8 %
A139921Primes of the form 3x^2+104y^2quadratic form50.1 %
A139923Primes of the form 8x^2+39y^2quadratic form50.9 %
A139926Primes of the form 13x^2+24y^2quadratic form50.6 %
A139928Primes of the form 2x^2+165y^2quadratic form53.5 %
A139929Primes of the form 3x^2+110y^2quadratic form53.3 %
A139930Primes of the form 5x^2+66y^2quadratic form54.2 %
A139931Primes of the form 6x^2+55y^2quadratic form54.2 %
A139932Primes of the form 10x^2+33y^2quadratic form53.3 %
A139933Primes of the form 11x^2+30y^2quadratic form54.0 %
A139934Primes of the form 15x^2+22y^2quadratic form53.5 %
A139936Primes of the form 3x^2+115y^2quadratic form51.6 %
A139937Primes of the form 5x^2+69y^2quadratic form50.9 %
A139940Primes of the form 15*x^2+23*y^2quadratic form51.1 %
A139943Primes of the form 3x^2+119y^2quadratic form45.6 %
A139945Primes of the form 7x^2+51y^2quadratic form44.9 %
A139947Primes of the form 17x^2+21y^2quadratic form44.4 %
A139950Primes of the form 5x^2+77y^2quadratic form45.7 %
A139951Primes of the form 7x^2+55y^2quadratic form45.9 %
A139953Primes of the form 11x^2+35y^2quadratic form46.2 %
A139956Primes of the form 3x^2+136y^2quadratic form47.7 %
A139958Primes of the form 8x^2+51y^2quadratic form47.1 %
A139961Primes of the form 17x^2+24y^2quadratic form47.9 %
A139963Primes of the form 2x^2+231y^2quadratic form48.5 %
A139964Primes of the form 3x^2+154y^2quadratic form47.3 %
A139965Primes of the form 6x^2+77y^2quadratic form47.4 %
A139966Primes of the form 7x^2+66y^2quadratic form47.3 %
A139967Primes of the form 11x^2+42y^2quadratic form48.4 %
A139968Primes of the form 14x^2+33y^2quadratic form47.4 %
A139969Primes of the form 21x^2+22y^2quadratic form48.4 %
A139971Primes of the form 5x^2+104y^2quadratic form48.6 %
A139972Primes of the form 8x^2+65y^2quadratic form47.9 %
A139974Primes of the form 13x^2+40y^2quadratic form48.1 %
A139978Primes of the form 5x^2+152y^2quadratic form47.7 %
A139979Primes of the form 8x^2+95y^2quadratic form47.8 %
A139981Primes of the form 19x^2+40y^2quadratic form47.6 %
A139984Primes of the form 3x^2+280y^2quadratic form54.3 %
A139985Primes of the form 4x^2+4xy+211y^2quadratic form53.6 %
A139986Primes of the form 5x^2+168y^2quadratic form54.4 %
A139987Primes of the form 7x^2+120y^2quadratic form54.5 %
A139988Primes of the form 8x^2+105y^2quadratic form54.5 %
A139991Primes of the form 15x^2+56y^2quadratic form53.7 %
A139993Primes of the form 21x^2+40y^2quadratic form54.9 %
A139994Primes of the form 24x^2+35y^2quadratic form55.0 %
A139999Primes of the form 3x^2+440y^2quadratic form58.3 %
A140001Primes of the form 5x^2+264y^2quadratic form58.7 %
A140002Primes of the form 8*x^2 + 165*y^2quadratic form58.4 %
A140004Primes of the form 11x^2+120y^2quadratic form58.9 %
A140006Primes of the form 15x^2+88y^2quadratic form58.2 %
A140008Primes of the form 24x^2+55y^2quadratic form58.8 %
A140010Primes of the form 33x^2+40y^2quadratic form58.3 %
A140015Primes of the form 3x^2+455y^2quadratic form56.1 %
A140016Primes of the form 5x^2+273y^2quadratic form56.1 %
A140018Primes of the form 7x^2+195y^2quadratic form56.3 %
A140020Primes of the form 13x^2+105y^2quadratic form56.0 %
A140022Primes of the form 15x^2+91y^2quadratic form55.9 %
A140023Primes of the form 21x^2+65y^2quadratic form56.2 %
A140026Primes of the form 35x^2+39y^2quadratic form55.5 %
A140029Primes of the form 3x^2+616y^2quadratic form52.3 %
A140031Primes of the form 7x^2+264y^2quadratic form52.4 %
A140032Primes of the form 8x^2+231y^2quadratic form53.3 %
A140034Primes of the form 11x^2+168y^2quadratic form52.7 %
A140036Primes of the form 21x^2+88y^2quadratic form53.0 %
A140037Primes of the form 24x^2+77y^2quadratic form52.2 %
A140040Primes of the form 33x^2+56y^2quadratic form52.1 %
A140065a(n) = (7*n^2 - 17*n + 12)/2polynomial100.0 %
A140066a(n) = (5*n^2 - 11*n + 8)/2polynomial100.0 %
A140090a(n) = n*(3*n + 7)/2polynomial100.0 %
A140091a(n) = 3*n*(n + 3)/2polynomial100.0 %
A140371Primes of the form 26k + 7primes42.8 %
A140372Primes of the form 26k + 9primes43.0 %
A140373Primes of the form 26*n+11primes42.9 %
A140374Primes of the form 26k + 15primes42.9 %
A140375Primes of the form 26n+23primes42.7 %
A140506Primes congruent to 11 or 19 mod 30primes37.5 %
A140533Primes congruent to 13 or 17 mod 30primes37.7 %
A140540Primes of form 17*n - 3primes44.3 %
A140541Primes of the form 17*k - 1primes44.6 %
A140542Primes of form 17*n - 6primes44.5 %
A140543Primes congruent to 15 mod 17primes44.5 %
A140544Primes of form 17*k + 2primes44.2 %
A140545Primes of form 17n + 6primes44.8 %
A140672a(n) = n*(3*n + 13)/2polynomial100.0 %
A140673a(n) = 3*n*(n + 5)/2polynomial100.0 %
A140674a(n) = n*(3*n + 17)/2polynomial100.0 %
A140675a(n) = n*(3*n + 19)/2polynomial100.0 %
A140676a(n) = n*(3*n + 4)polynomial100.0 %
A140677a(n) = n*(3*n + 8)polynomial100.0 %
A140678a(n) = n*(3*n + 10)polynomial100.0 %
A140679a(n) = n*(3*n+14)polynomial100.0 %
A140680a(n) = n*(3*n+16)polynomial100.0 %
A140681a(n) = 3*n*(n+6)polynomial100.0 %
A140689a(n) = n*(3*n + 20)polynomial100.0 %
A140840Primes of the form 210n+11primes63.0 %
A140841Primes of the form 210n + 13primes62.6 %
A140842Primes of the form 210k + 17primes62.8 %
A140843Primes of the form 210k + 19primes63.0 %
A140844Primes of the form 210k + 23primes63.1 %
A140845Primes of the form 210k + 29primes62.7 %
A140846Primes of the form 210k + 31primes62.7 %
A140847Primes of the form 210k + 37primes62.7 %
A140848Primes of the form 210k + 41primes63.0 %
A140849Primes of the form 210k + 43primes62.7 %
A140850Primes of the form 210k + 47primes62.9 %
A140851Primes of the form 210k + 53primes62.7 %
A140852Primes of the form 210k + 59primes62.8 %
A140854Primes of the form 210k + 61primes62.8 %
A140855Primes of the form 210k + 67primes62.8 %
A140856Primes of the form 210n+71primes62.8 %
A140857Primes of the form 210k + 73primes62.9 %
A141194Primes of the form 16k+7primes37.9 %
A141195Primes of the form 16k+11primes38.2 %
A141196Primes of the form 16k+13primes38.6 %
A141489Numbers k such that k^2 + k + 257 is primeprime values20.0 %
A141563Primes of the form 2*3*5*7*n+79primes62.9 %
A141570Primes of the form 2*3*5*7*n+83primes62.9 %
A141631a(n) = 3*n^2 - 4*n + 3polynomial100.0 %
A141759a(n) = 16n^2 + 32n + 15polynomial100.0 %
A141849Primes congruent to 1 mod 11primes41.6 %
A141850Primes congruent to 3 mod 11primes41.7 %
A141851Primes congruent to 4 mod 11primes41.7 %
A141852Primes congruent to 5 mod 11primes42.0 %
A141853Primes congruent to 6 mod 11primes41.5 %
A141854Primes congruent to 7 mod 11primes41.9 %
A141855Primes congruent to 8 mod 11primes41.7 %
A141856Primes congruent to 9 mod 11primes41.8 %
A141857Primes congruent to 10 mod 11primes41.8 %
A141859Primes congruent to 12 mod 13primes42.6 %
A141865Primes congruent to 13 mod 17primes44.2 %
A141868Primes congruent to 1 mod 19primes45.0 %
A141869Primes congruent to 2 mod 19primes44.9 %
A141870Primes congruent to 4 mod 19primes45.1 %
A141871Primes congruent to 6 mod 19primes45.2 %
A141872Primes congruent to 7 mod 19primes45.2 %
A141873Primes congruent to 8 mod 19primes44.9 %
A141874Primes congruent to 9 mod 19primes45.2 %
A141875Primes congruent to 10 mod 19primes45.1 %
A141876Primes congruent to 11 mod 19primes45.1 %
A141877Primes congruent to 12 mod 19primes45.2 %
A141878Primes congruent to 13 mod 19primes45.2 %
A141879Primes congruent to 14 mod 19primes45.2 %
A141880Primes congruent to 15 mod 19primes44.9 %
A141881Primes congruent to 1 mod 20primes41.9 %
A141882Primes congruent to 7 mod 20primes42.0 %
A141883Primes congruent to 9 mod 20primes42.0 %
A141884Primes congruent to 11 mod 20primes41.9 %
A141885Primes congruent to 13 mod 20primes41.7 %
A141886Primes congruent to 17 mod 20primes41.9 %
A141887Primes congruent to 19 mod 20primes41.8 %
A141888Primes congruent to 2 mod 21primes50.2 %
A141889Primes congruent to 4 mod 21primes50.0 %
A141890Primes congruent to 5 mod 21primes50.2 %
A141891Primes congruent to 8 mod 21primes50.1 %
A141892Primes congruent to 10 mod 21primes50.0 %
A141893Primes congruent to 11 mod 21primes49.8 %
A141894Primes congruent to 13 mod 21primes50.0 %
A141895Primes congruent to 16 mod 21primes50.1 %
A141896Primes congruent to 17 mod 21primes50.0 %
A141897Primes congruent to 19 mod 21primes50.0 %
A141898Primes congruent to 20 mod 21primes50.0 %
A141899Primes of the form 2*3*5*7*k + 97primes63.1 %
A141908Primes congruent to 2 mod 23primes46.5 %
A141909Primes congruent to 4 mod 23primes46.4 %
A141910Primes congruent to 6 mod 23primes46.1 %
A141911Primes congruent to 7 mod 23primes46.3 %
A141912Primes congruent to 8 mod 23primes46.5 %
A141913Primes congruent to 9 mod 23primes46.2 %
A141914Primes congruent to 10 mod 23primes46.3 %
A141915Primes congruent to 11 mod 23primes46.4 %
A141916Primes congruent to 12 mod 23primes46.2 %
A141917Primes congruent to 13 mod 23primes46.3 %
A141918Primes congruent to 14 mod 23primes46.8 %
A141919Primes congruent to 15 mod 23primes46.3 %
A141920Primes congruent to 16 mod 23primes46.1 %
A141921Primes congruent to 17 mod 23primes46.2 %
A141922Primes congruent to 18 mod 23primes46.5 %
A141923Primes congruent to 19 mod 23primes46.2 %
A141924Primes congruent to 20 mod 23primes46.2 %
A141925Primes congruent to 21 mod 23primes46.2 %
A141926Primes congruent to 22 mod 23primes46.3 %
A141927Primes congruent to 1 mod 25primes48.2 %
A141928Primes congruent to 2 mod 25primes48.5 %
A141929Primes congruent to 3 mod 25primes48.1 %
A141930Primes congruent to 4 mod 25primes48.5 %
A141931Primes congruent to 6 mod 25primes48.1 %
A141932Primes congruent to 7 mod 25primes48.3 %
A141933Primes congruent to 8 mod 25primes48.1 %
A141934Primes congruent to 9 mod 25primes48.4 %
A141935Primes congruent to 11 mod 25primes48.6 %
A141936Primes congruent to 12 mod 25primes48.0 %
A141937Primes congruent to 13 mod 25primes48.1 %
A141938Primes congruent to 14 mod 25primes48.3 %
A141939Primes congruent to 16 mod 25primes48.1 %
A141940Primes congruent to 17 mod 25primes48.4 %
A141941Primes congruent to 18 mod 25primes48.2 %
A141942Primes congruent to 19 mod 25primes48.0 %
A141943Primes congruent to 21 mod 25primes48.4 %
A141944Primes congruent to 22 mod 25primes48.3 %
A141945Primes congruent to 23 mod 25primes48.3 %
A141946Primes congruent to 24 mod 25primes48.4 %
A141948Primes congruent to 1 mod 27primes49.9 %
A141949Primes congruent to 2 mod 27primes50.0 %
A141950Primes congruent to 4 mod 27primes50.0 %
A141951Primes congruent to 5 mod 27primes50.0 %
A141952Primes congruent to 7 mod 27primes50.0 %
A141953Primes congruent to 8 mod 27primes50.0 %
A141954Primes congruent to 10 mod 27primes49.7 %
A141955Primes congruent to 11 mod 27primes50.0 %
A141956Primes congruent to 13 mod 27primes50.1 %
A141957Primes congruent to 14 mod 27primes49.8 %
A141958Primes congruent to 16 mod 27primes50.0 %
A141959Primes congruent to 17 mod 27primes49.9 %
A141960Primes congruent to 19 mod 27primes50.0 %
A141961Primes congruent to 20 mod 27primes49.8 %
A141962Primes congruent to 22 mod 27primes50.1 %
A141963Primes congruent to 23 mod 27primes49.9 %
A141964Primes congruent to 25 mod 27primes49.5 %
A141965Primes congruent to 26 mod 27primes50.1 %
A141966Primes congruent to 3 mod 28primes44.1 %
A141967Primes congruent to 5 mod 28primes43.7 %
A141968Primes congruent to 9 mod 28primes43.7 %
A141969Primes congruent to 11 mod 28primes43.9 %
A141970Primes congruent to 13 mod 28primes43.8 %
A141971Primes congruent to 15 mod 28primes44.0 %
A141972Primes congruent to 17 mod 28primes43.7 %
A141973Primes congruent to 19 mod 28primes44.1 %
A141974Primes congruent to 23 mod 28primes43.9 %
A141975Primes congruent to 25 mod 28primes43.9 %
A141976Primes congruent to 27 mod 28primes43.6 %
A141977Primes congruent to 1 mod 29primes47.7 %
A141978Primes congruent to 2 mod 29primes47.6 %
A141979Primes congruent to 3 mod 29primes47.5 %
A141980Primes congruent to 4 mod 29primes47.9 %
A141981Primes congruent to 5 mod 29primes47.8 %
A141982Primes congruent to 6 mod 29primes47.8 %
A141983Primes congruent to 7 mod 29primes47.8 %
A141984Primes congruent to 8 mod 29primes47.6 %
A141985Primes congruent to 9 mod 29primes47.7 %
A141986Primes congruent to 10 mod 29primes48.0 %
A141987Primes congruent to 11 mod 29primes47.9 %
A141988Primes congruent to 12 mod 29primes47.7 %
A141989Primes congruent to 13 mod 29primes47.9 %
A141990Primes congruent to 14 mod 29primes47.7 %
A141991Primes congruent to 15 mod 29primes47.6 %
A141992Primes congruent to 16 mod 29primes47.9 %
A141993Primes congruent to 17 mod 29primes48.2 %
A141994Primes congruent to 18 mod 29primes47.9 %
A141995Primes congruent to 19 mod 29primes47.7 %
A141996Primes congruent to 20 mod 29primes47.7 %
A141997Primes congruent to 21 mod 29primes47.9 %
A141998Primes congruent to 22 mod 29primes48.0 %
A141999Primes congruent to 23 mod 29primes47.9 %
A142000Primes congruent to 24 mod 29primes47.8 %
A142001Primes congruent to 25 mod 29primes47.9 %
A142002Primes congruent to 26 mod 29primes47.9 %
A142003Primes congruent to 27 mod 29primes47.8 %
A142004Primes congruent to 28 mod 29primes47.6 %
A142005Primes congruent to 1 mod 31primes48.2 %
A142006Primes congruent to 2 mod 31primes47.9 %
A142007Primes congruent to 3 mod 31primes47.7 %
A142008Primes congruent to 4 mod 31primes48.5 %
A142009Primes congruent to 5 mod 31primes48.2 %
A142010Primes congruent to 6 mod 31primes48.1 %
A142011Primes congruent to 7 mod 31primes48.2 %
A142012Primes congruent to 8 mod 31primes48.1 %
A142013Primes congruent to 9 mod 31primes48.1 %
A142014Primes congruent to 10 mod 31primes48.2 %
A142015Primes congruent to 11 mod 31primes48.1 %
A142016Primes congruent to 12 mod 31primes48.4 %
A142017Primes congruent to 13 mod 31primes48.2 %
A142018Primes congruent to 14 mod 31primes48.4 %
A142019Primes congruent to 15 mod 31primes48.2 %
A142020Primes congruent to 16 mod 31primes48.0 %
A142021Primes congruent to 17 mod 31primes48.3 %
A142022Primes congruent to 18 mod 31primes48.2 %
A142023Primes congruent to 19 mod 31primes47.9 %
A142024Primes congruent to 20 mod 31primes48.2 %
A142025Primes congruent to 21 mod 31primes48.1 %
A142026Primes congruent to 22 mod 31primes48.3 %
A142027Primes congruent to 23 mod 31primes48.3 %
A142028Primes congruent to 24 mod 31primes48.2 %
A142029Primes congruent to 25 mod 31primes48.0 %
A142030Primes congruent to 26 mod 31primes48.5 %
A142031Primes congruent to 27 mod 31primes48.0 %
A142032Primes congruent to 28 mod 31primes48.5 %
A142033Primes congruent to 29 mod 31primes48.2 %
A142034Primes congruent to 30 mod 31primes48.3 %
A142035Primes congruent to 3 mod 32primes43.3 %
A142036Primes congruent to 5 mod 32primes43.3 %
A142037Primes congruent to 7 mod 32primes43.1 %
A142038Primes congruent to 9 mod 32primes43.2 %
A142039Primes congruent to 11 mod 32primes43.0 %
A142040Primes congruent to 13 mod 32primes43.3 %
A142041Primes congruent to 15 mod 32primes43.2 %
A142042Primes congruent to 19 mod 32primes43.2 %
A142043Primes congruent to 21 mod 32primes43.2 %
A142044Primes congruent to 23 mod 32primes43.2 %
A142045Primes congruent to 25 mod 32primes43.1 %
A142046Primes congruent to 27 mod 32primes43.1 %
A142047Primes congruent to 29 mod 32primes42.8 %
A142049Primes congruent to 1 mod 33primes52.5 %
A142050Primes congruent to 2 mod 33primes52.5 %
A142051Primes congruent to 4 mod 33primes52.5 %
A142052Primes congruent to 5 mod 33primes52.7 %
A142053Primes congruent to 7 mod 33primes52.5 %
A142054Primes congruent to 8 mod 33primes52.6 %
A142055Primes congruent to 10 mod 33primes52.8 %
A142056Primes congruent to 13 mod 33primes52.5 %
A142057Primes congruent to 14 mod 33primes52.5 %
A142058Primes congruent to 16 mod 33primes52.7 %
A142059Primes congruent to 17 mod 33primes52.6 %
A142060Primes congruent to 19 mod 33primes52.5 %
A142061Primes congruent to 20 mod 33primes52.5 %
A142062Primes congruent to 23 mod 33primes52.6 %
A142063Primes congruent to 25 mod 33primes52.5 %
A142064Primes congruent to 26 mod 33primes52.6 %
A142065Primes congruent to 28 mod 33primes52.4 %
A142066Primes congruent to 29 mod 33primes52.9 %
A142067Primes congruent to 31 mod 33primes52.6 %
A142068Primes congruent to 32 mod 33primes52.6 %
A142076Primes congruent to 1 mod 35primes52.2 %
A142077Primes congruent to 2 mod 35primes52.0 %
A142078Primes congruent to 3 mod 35primes52.0 %
A142079Primes congruent to 4 mod 35primes52.4 %
A142080Primes congruent to 6 mod 35primes52.3 %
A142081Primes congruent to 8 mod 35primes52.3 %
A142082Primes congruent to 9 mod 35primes52.1 %
A142083Primes congruent to 11 mod 35primes52.3 %
A142084Primes congruent to 12 mod 35primes52.2 %
A142085Primes congruent to 13 mod 35primes52.3 %
A142086Primes congruent to 16 mod 35primes52.1 %
A142087Primes congruent to 17 mod 35primes51.9 %
A142088Primes congruent to 18 mod 35primes52.4 %
A142089Primes congruent to 19 mod 35primes52.3 %
A142090Primes congruent to 22 mod 35primes52.4 %
A142091Primes congruent to 23 mod 35primes52.1 %
A142092Primes congruent to 24 mod 35primes52.2 %
A142093Primes congruent to 26 mod 35primes52.3 %
A142094Primes congruent to 27 mod 35primes52.3 %
A142095Primes congruent to 29 mod 35primes52.4 %
A142096Primes congruent to 31 mod 35primes52.0 %
A142097Primes congruent to 32 mod 35primes51.9 %
A142098Primes congruent to 33 mod 35primes52.2 %
A142099Primes congruent to 34 mod 35primes52.2 %
A142101Primes congruent to 5 mod 36primes47.6 %
A142102Primes congruent to 7 mod 36primes47.5 %
A142103Primes congruent to 11 mod 36primes47.5 %
A142104Primes congruent to 13 mod 36primes47.4 %
A142105Primes congruent to 17 mod 36primes47.3 %
A142106Primes congruent to 19 mod 36primes47.3 %
A142107Primes congruent to 23 mod 36primes47.4 %
A142108Primes congruent to 25 mod 36primes47.1 %
A142109Primes congruent to 29 mod 36primes47.3 %
A142110Primes congruent to 31 mod 36primes47.4 %
A142111Primes congruent to 35 mod 36primes47.5 %
A142112Primes congruent to 2 mod 37primes49.3 %
A142113Primes congruent to 4 mod 37primes49.6 %
A142114Primes congruent to 5 mod 37primes49.5 %
A142115Primes congruent to 6 mod 37primes49.4 %
A142116Primes congruent to 7 mod 37primes49.4 %
A142117Primes congruent to 8 mod 37primes49.2 %
A142118Primes congruent to 9 mod 37primes49.2 %
A142119Primes congruent to 10 mod 37primes49.8 %
A142120Primes congruent to 11 mod 37primes49.6 %
A142121Primes congruent to 12 mod 37primes49.3 %
A142122Primes congruent to 13 mod 37primes49.2 %
A142123Primes congruent to 14 mod 37primes49.6 %
A142124Primes congruent to 15 mod 37primes49.4 %
A142125Primes congruent to 16 mod 37primes49.3 %
A142126Primes congruent to 17 mod 37primes49.3 %
A142127Primes congruent to 18 mod 37primes49.6 %
A142128Primes congruent to 19 mod 37primes49.4 %
A142129Primes congruent to 20 mod 37primes49.6 %
A142130Primes congruent to 21 mod 37primes49.3 %
A142131Primes congruent to 22 mod 37primes49.6 %
A142132Primes congruent to 23 mod 37primes49.3 %
A142133Primes congruent to 24 mod 37primes49.6 %
A142134Primes congruent to 25 mod 37primes49.5 %
A142135Primes congruent to 26 mod 37primes49.6 %
A142136Primes congruent to 27 mod 37primes49.5 %
A142137Primes congruent to 28 mod 37primes49.5 %
A142138Primes congruent to 29 mod 37primes49.2 %
A142139Primes congruent to 30 mod 37primes49.4 %
A142140Primes congruent to 31 mod 37primes49.4 %
A142141Primes congruent to 32 mod 37primes49.5 %
A142142Primes congruent to 33 mod 37primes49.7 %
A142143Primes congruent to 34 mod 37primes49.6 %
A142144Primes congruent to 35 mod 37primes49.2 %
A142145Primes congruent to 36 mod 37primes49.2 %
A142159Primes congruent to 1 mod 39primes53.5 %
A142160Primes congruent to 2 mod 39primes53.5 %
A142161Primes congruent to 4 mod 39primes53.4 %
A142162Primes congruent to 5 mod 39primes53.6 %
A142163Primes congruent to 7 mod 39primes53.6 %
A142164Primes congruent to 8 mod 39primes53.7 %
A142165Primes congruent to 10 mod 39primes53.4 %
A142166Primes congruent to 11 mod 39primes53.5 %
A142167Primes congruent to 14 mod 39primes53.6 %
A142168Primes congruent to 16 mod 39primes53.4 %
A142169Primes congruent to 17 mod 39primes53.7 %
A142170Primes congruent to 19 mod 39primes53.8 %
A142171Primes congruent to 20 mod 39primes53.6 %
A142172Primes congruent to 22 mod 39primes53.4 %
A142173Primes congruent to 23 mod 39primes53.5 %
A142174Primes congruent to 25 mod 39primes53.3 %
A142176Primes congruent to 29 mod 39primes53.3 %
A142177Primes congruent to 31 mod 39primes53.6 %
A142178Primes congruent to 32 mod 39primes53.3 %
A142179Primes congruent to 34 mod 39primes53.4 %
A142180Primes congruent to 35 mod 39primes53.5 %
A142181Primes congruent to 37 mod 39primes53.7 %
A142182Primes congruent to 38 mod 39primes53.3 %
A142183Primes congruent to 1 mod 40primes46.5 %
A142184Primes congruent to 3 mod 40primes47.1 %
A142185Primes congruent to 7 mod 40primes46.6 %
A142186Primes congruent to 9 mod 40primes47.0 %
A142187Primes congruent to 11 mod 40primes46.9 %
A142188Primes congruent to 13 mod 40primes46.6 %
A142189Primes congruent to 17 mod 40primes47.1 %
A142190Primes congruent to 19 mod 40primes46.7 %
A142191Primes congruent to 21 mod 40primes46.8 %
A142192Primes congruent to 23 mod 40primes46.7 %
A142193Primes congruent to 27 mod 40primes46.7 %
A142194Primes congruent to 29 mod 40primes47.1 %
A142195Primes congruent to 31 mod 40primes46.9 %
A142196Primes congruent to 33 mod 40primes46.8 %
A142197Primes congruent to 37 mod 40primes46.8 %
A142198Primes congruent to 39 mod 40primes47.0 %
A142199Primes congruent to 2 mod 41primes50.0 %
A142200Primes congruent to 3 mod 41primes50.0 %
A142201Primes congruent to 4 mod 41primes50.1 %
A142202Primes congruent to 5 mod 41primes50.2 %
A142203Primes congruent to 6 mod 41primes50.3 %
A142204Primes congruent to 7 mod 41primes49.8 %
A142205Primes congruent to 8 mod 41primes50.1 %
A142206Primes congruent to 9 mod 41primes50.2 %
A142207Primes congruent to 10 mod 41primes50.1 %
A142208Primes congruent to 11 mod 41primes50.0 %
A142209Primes congruent to 12 mod 41primes50.3 %
A142210Primes congruent to 13 mod 41primes50.0 %
A142211Primes congruent to 14 mod 41primes50.2 %
A142212Primes congruent to 15 mod 41primes50.2 %
A142213Primes congruent to 16 mod 41primes50.1 %
A142214Primes congruent to 17 mod 41primes50.1 %
A142215Primes congruent to 18 mod 41primes50.1 %
A142216Primes congruent to 19 mod 41primes50.1 %
A142217Primes congruent to 20 mod 41primes50.2 %
A142218Primes congruent to 21 mod 41primes50.0 %
A142219Primes congruent to 22 mod 41primes50.2 %
A142220Primes congruent to 23 mod 41primes50.1 %
A142221Primes congruent to 24 mod 41primes50.1 %
A142222Primes congruent to 25 mod 41primes49.7 %
A142223Primes congruent to 26 mod 41primes49.8 %
A142224Primes congruent to 27 mod 41primes50.3 %
A142225Primes congruent to 28 mod 41primes49.8 %
A142226Primes congruent to 29 mod 41primes50.1 %
A142227Primes congruent to 30 mod 41primes50.1 %
A142228Primes congruent to 31 mod 41primes50.0 %
A142229Primes congruent to 32 mod 41primes50.3 %
A142230Primes congruent to 33 mod 41primes50.1 %
A142250Primes congruent to 1 mod 43primes50.5 %
A142251Primes congruent to 2 mod 43primes50.7 %
A142252Primes congruent to 3 mod 43primes50.5 %
A142253Primes congruent to 4 mod 43primes50.2 %
A142254Primes congruent to 5 mod 43primes50.3 %
A142255Primes congruent to 6 mod 43primes50.1 %
A142256Primes congruent to 7 mod 43primes50.6 %
A142257Primes congruent to 8 mod 43primes50.1 %
A142258Primes congruent to 9 mod 43primes50.4 %
A142259Primes congruent to 10 mod 43primes50.3 %
A142260Primes congruent to 11 mod 43primes50.2 %
A142261Primes congruent to 12 mod 43primes50.3 %
A142262Primes congruent to 13 mod 43primes50.4 %
A142263Primes congruent to 14 mod 43primes50.5 %
A142264Primes congruent to 15 mod 43primes50.7 %
A142265Primes congruent to 16 mod 43primes50.3 %
A142266Primes congruent to 17 mod 43primes50.4 %
A142267Primes congruent to 18 mod 43primes50.2 %
A142268Primes congruent to 19 mod 43primes50.3 %
A142269Primes congruent to 20 mod 43primes50.6 %
A142270Primes congruent to 21 mod 43primes50.6 %
A142271Primes congruent to 22 mod 43primes50.3 %
A142272Primes congruent to 23 mod 43primes50.5 %
A142273Primes congruent to 24 mod 43primes50.2 %
A142274Primes congruent to 25 mod 43primes50.7 %
A142275Primes congruent to 26 mod 43primes50.4 %
A142276Primes congruent to 27 mod 43primes50.8 %
A142277Primes congruent to 28 mod 43primes50.3 %
A142278Primes congruent to 29 mod 43primes50.3 %
A142279Primes congruent to 30 mod 43primes50.4 %
A142280Primes congruent to 31 mod 43primes50.3 %
A142281Primes congruent to 32 mod 43primes50.5 %
A142292Primes congruent to 1 mod 44primes46.4 %
A142293Primes congruent to 3 mod 44primes46.4 %
A142294Primes congruent to 5 mod 44primes46.6 %
A142295Primes congruent to 7 mod 44primes46.6 %
A142296Primes congruent to 9 mod 44primes46.0 %
A142297Primes congruent to 13 mod 44primes46.5 %
A142298Primes congruent to 15 mod 44primes46.4 %
A142299Primes congruent to 17 mod 44primes46.2 %
A142300Primes congruent to 19 mod 44primes46.3 %
A142301Primes congruent to 21 mod 44primes46.6 %
A142302Primes congruent to 23 mod 44primes46.5 %
A142303Primes congruent to 25 mod 44primes46.3 %
A142304Primes congruent to 27 mod 44primes46.4 %
A142305Primes congruent to 29 mod 44primes46.6 %
A142306Primes congruent to 31 mod 44primes46.5 %
A142307Primes congruent to 35 mod 44primes46.5 %
A142308Primes congruent to 37 mod 44primes46.6 %
A142309Primes congruent to 39 mod 44primes46.5 %
A142310Primes congruent to 41 mod 44primes46.4 %
A142311Primes congruent to 43 mod 44primes46.6 %
A142312Primes congruent to 1 mod 45primes55.4 %
A142313Primes congruent to 2 mod 45primes55.8 %
A142314Primes congruent to 4 mod 45primes55.6 %
A142315Primes congruent to 7 mod 45primes55.4 %
A142316Primes congruent to 8 mod 45primes55.2 %
A142317Primes congruent to 11 mod 45primes55.7 %
A142318Primes congruent to 13 mod 45primes55.5 %
A142319Primes congruent to 14 mod 45primes55.5 %
A142320Primes congruent to 16 mod 45primes55.3 %
A142321Primes congruent to 17 mod 45primes55.5 %
A142322Primes congruent to 19 mod 45primes55.7 %
A142323Primes congruent to 22 mod 45primes55.4 %
A142324Primes congruent to 23 mod 45primes55.4 %
A142325Primes congruent to 26 mod 45primes55.6 %
A142326Primes congruent to 28 mod 45primes55.3 %
A142327Primes congruent to 29 mod 45primes55.5 %
A142328Primes congruent to 31 mod 45primes55.2 %
A142329Primes congruent to 32 mod 45primes55.7 %
A142330Primes congruent to 34 mod 45primes55.4 %
A142331Primes congruent to 37 mod 45primes55.2 %
A142332Primes congruent to 38 mod 45primes55.5 %
A142333Primes congruent to 41 mod 45primes55.6 %
A142334Primes congruent to 43 mod 45primes55.3 %
A142335Primes congruent to 44 mod 45primes55.5 %
A142357Primes congruent to 6 mod 47primes51.1 %
A142358Primes congruent to 7 mod 47primes51.1 %
A142359Primes congruent to 8 mod 47primes50.8 %
A142360Primes congruent to 9 mod 47primes51.2 %
A142362Primes congruent to 11 mod 47primes51.3 %
A142363Primes congruent to 12 mod 47primes50.8 %
A142366Primes congruent to 15 mod 47primes50.9 %
A142367Primes congruent to 16 mod 47primes51.1 %
A142368Primes congruent to 17 mod 47primes51.1 %
A142369Primes congruent to 18 mod 47primes51.3 %
A142370Primes congruent to 19 mod 47primes51.1 %
A142371Primes congruent to 20 mod 47primes50.9 %
A142372Primes congruent to 21 mod 47primes51.1 %
A142374Primes congruent to 23 mod 47primes50.8 %
A142398Primes congruent to 1 mod 48primes49.4 %
A142399Primes congruent to 5 mod 48primes49.5 %
A142400Primes congruent to 7 mod 48primes49.0 %
A142401Primes congruent to 11 mod 48primes49.0 %
A142402Primes congruent to 13 mod 48primes49.4 %
A142403Primes congruent to 17 mod 48primes49.4 %
A142404Primes congruent to 19 mod 48primes49.3 %
A142405Primes congruent to 23 mod 48primes49.3 %
A142406Primes congruent to 25 mod 48primes48.9 %
A142407Primes congruent to 29 mod 48primes49.4 %
A142408Primes congruent to 31 mod 48primes49.3 %
A142409Primes congruent to 35 mod 48primes48.9 %
A142410Primes congruent to 37 mod 48primes49.3 %
A142411Primes congruent to 41 mod 48primes49.0 %
A142412Primes congruent to 43 mod 48primes49.2 %
A142413Primes congruent to 47 mod 48primes49.3 %
A142414Primes congruent to 1 mod 49primes52.5 %
A142415Primes congruent to 2 mod 49primes52.4 %
A142416Primes congruent to 3 mod 49primes52.5 %
A142417Primes congruent to 4 mod 49primes52.2 %
A142418Primes congruent to 5 mod 49primes52.5 %
A142419Primes congruent to 6 mod 49primes52.3 %
A142420Primes congruent to 8 mod 49primes52.5 %
A142421Primes congruent to 9 mod 49primes52.5 %
A142422Primes congruent to 10 mod 49primes52.4 %
A142423Primes congruent to 11 mod 49primes52.4 %
A142424Primes congruent to 12 mod 49primes52.4 %
A142425Primes congruent to 13 mod 49primes52.4 %
A142426Primes congruent to 15 mod 49primes52.4 %
A142427Primes congruent to 16 mod 49primes52.5 %
A142428Primes congruent to 17 mod 49primes52.4 %
A142429Primes congruent to 18 mod 49primes52.5 %
A142430Primes congruent to 19 mod 49primes52.5 %
A142431Primes congruent to 20 mod 49primes52.6 %
A142432Primes congruent to 22 mod 49primes52.3 %
A142433Primes congruent to 23 mod 49primes52.6 %
A142434Primes congruent to 24 mod 49primes52.6 %
A142435Primes congruent to 25 mod 49primes52.5 %
A142436Primes congruent to 26 mod 49primes52.5 %
A142437Primes congruent to 27 mod 49primes52.4 %
A142438Primes congruent to 29 mod 49primes52.4 %
A142439Primes congruent to 30 mod 49primes52.4 %
A142440Primes congruent to 31 mod 49primes52.0 %
A142441Primes congruent to 32 mod 49primes52.5 %
A142442Primes congruent to 33 mod 49primes52.5 %
A142443Primes congruent to 34 mod 49primes52.5 %
A142444Primes congruent to 36 mod 49primes52.6 %
A142445Primes congruent to 37 mod 49primes52.5 %
A142446Primes congruent to 38 mod 49primes52.3 %
A142447Primes congruent to 39 mod 49primes52.5 %
A142448Primes congruent to 40 mod 49primes52.4 %
A142449Primes congruent to 41 mod 49primes52.3 %
A142450Primes congruent to 43 mod 49primes52.3 %
A142451Primes congruent to 44 mod 49primes52.3 %
A142452Primes congruent to 45 mod 49primes52.6 %
A142453Primes congruent to 46 mod 49primes52.5 %
A142454Primes congruent to 47 mod 49primes52.5 %
A142455Primes congruent to 48 mod 49primes52.2 %
A142476Primes congruent to 1 mod 51primes55.1 %
A142477Primes congruent to 2 mod 51primes54.9 %
A142478Primes congruent to 4 mod 51primes55.1 %
A142479Primes congruent to 5 mod 51primes55.2 %
A142480Primes congruent to 7 mod 51primes55.3 %
A142481Primes congruent to 8 mod 51primes55.1 %
A142482Primes congruent to 10 mod 51primes55.1 %
A142483Primes congruent to 11 mod 51primes55.2 %
A142484Primes congruent to 13 mod 51primes55.2 %
A142485Primes congruent to 14 mod 51primes55.4 %
A142486Primes congruent to 16 mod 51primes55.2 %
A142487Primes congruent to 19 mod 51primes55.2 %
A142488Primes congruent to 20 mod 51primes55.2 %
A142489Primes congruent to 22 mod 51primes55.3 %
A142490Primes congruent to 23 mod 51primes55.2 %
A142491Primes congruent to 25 mod 51primes55.4 %
A142492Primes congruent to 26 mod 51primes55.4 %
A142493Primes congruent to 28 mod 51primes55.1 %
A142494Primes congruent to 29 mod 51primes55.1 %
A142495Primes congruent to 31 mod 51primes55.3 %
A142496Primes congruent to 32 mod 51primes55.0 %
A142497Primes congruent to 35 mod 51primes55.2 %
A142498Primes congruent to 37 mod 51primes55.0 %
A142499Primes congruent to 38 mod 51primes55.3 %
A142500Primes congruent to 40 mod 51primes55.3 %
A142501Primes congruent to 41 mod 51primes55.6 %
A142502Primes congruent to 43 mod 51primes55.4 %
A142503Primes congruent to 44 mod 51primes55.2 %
A142504Primes congruent to 46 mod 51primes55.3 %
A142505Primes congruent to 47 mod 51primes55.1 %
A142506Primes congruent to 49 mod 51primes55.2 %
A142507Primes congruent to 50 mod 51primes55.1 %
A142508Primes congruent to 1 mod 52primes47.6 %
A142509Primes congruent to 3 mod 52primes47.2 %
A142510Primes congruent to 5 mod 52primes47.4 %
A142511Primes congruent to 7 mod 52primes47.4 %
A142512Primes congruent to 9 mod 52primes47.6 %
A142513Primes congruent to 11 mod 52primes47.3 %
A142514Primes congruent to 15 mod 52primes47.2 %
A142515Primes congruent to 17 mod 52primes47.3 %
A142516Primes congruent to 19 mod 52primes47.6 %
A142517Primes congruent to 21 mod 52primes47.5 %
A142518Primes congruent to 23 mod 52primes47.4 %
A142519Primes congruent to 25 mod 52primes47.4 %
A142520Primes congruent to 27 mod 52primes47.5 %
A142521Primes congruent to 29 mod 52primes47.4 %
A142522Primes congruent to 31 mod 52primes47.6 %
A142523Primes congruent to 33 mod 52primes47.4 %
A142524Primes congruent to 35 mod 52primes47.5 %
A142525Primes congruent to 37 mod 52primes47.6 %
A142526Primes congruent to 41 mod 52primes47.4 %
A142527Primes congruent to 43 mod 52primes47.4 %
A142528Primes congruent to 45 mod 52primes47.5 %
A142529Primes congruent to 47 mod 52primes47.6 %
A142530Primes congruent to 49 mod 52primes47.4 %
A142531Primes congruent to 51 mod 52primes47.6 %
A142601Primes congruent to 1 mod 55primes55.0 %
A142602Primes congruent to 2 mod 55primes55.0 %
A142603Primes congruent to 3 mod 55primes54.9 %
A142604Primes congruent to 4 mod 55primes54.6 %
A142605Primes congruent to 6 mod 55primes54.6 %
A142606Primes congruent to 7 mod 55primes54.8 %
A142607Primes congruent to 8 mod 55primes54.8 %
A142608Primes congruent to 9 mod 55primes54.7 %
A142609Primes congruent to 12 mod 55primes55.0 %
A142610Primes congruent to 13 mod 55primes54.8 %
A142611Primes congruent to 14 mod 55primes54.7 %
A142612Primes congruent to 16 mod 55primes54.6 %
A142613Primes congruent to 17 mod 55primes54.9 %
A142614Primes congruent to 18 mod 55primes54.7 %
A142615Primes congruent to 19 mod 55primes54.9 %
A142616Primes congruent to 21 mod 55primes55.0 %
A142617Primes congruent to 23 mod 55primes54.5 %
A142618Primes congruent to 24 mod 55primes54.6 %
A142619Primes congruent to 26 mod 55primes54.7 %
A142620Primes congruent to 27 mod 55primes55.1 %
A142621Primes congruent to 28 mod 55primes54.6 %
A142622Primes congruent to 29 mod 55primes54.8 %
A142623Primes congruent to 31 mod 55primes54.5 %
A142624Primes congruent to 32 mod 55primes54.5 %
A142625Primes congruent to 34 mod 55primes54.8 %
A142626Primes congruent to 36 mod 55primes54.9 %
A142627Primes congruent to 37 mod 55primes54.6 %
A142628Primes congruent to 38 mod 55primes54.7 %
A142629Primes congruent to 39 mod 55primes54.7 %
A142630Primes congruent to 41 mod 55primes54.7 %
A142631Primes congruent to 42 mod 55primes54.6 %
A142632Primes congruent to 43 mod 55primes54.9 %
A142633Primes congruent to 46 mod 55primes54.5 %
A142634Primes congruent to 47 mod 55primes54.6 %
A142635Primes congruent to 48 mod 55primes54.8 %
A142636Primes congruent to 49 mod 55primes54.9 %
A142637Primes congruent to 51 mod 55primes54.6 %
A142638Primes congruent to 52 mod 55primes54.7 %
A142639Primes congruent to 53 mod 55primes54.5 %
A142640Primes congruent to 54 mod 55primes54.6 %
A142641Primes congruent to 1 mod 56primes48.6 %
A142642Primes congruent to 3 mod 56primes48.4 %
A142643Primes congruent to 5 mod 56primes48.6 %
A142644Primes congruent to 9 mod 56primes48.8 %
A142645Primes congruent to 11 mod 56primes48.5 %
A142646Primes congruent to 13 mod 56primes49.0 %
A142647Primes congruent to 15 mod 56primes48.6 %
A142648Primes congruent to 17 mod 56primes48.3 %
A142649Primes congruent to 19 mod 56primes48.6 %
A142650Primes congruent to 23 mod 56primes48.7 %
A142651Primes congruent to 25 mod 56primes48.5 %
A142652Primes congruent to 27 mod 56primes48.7 %
A142653Primes congruent to 29 mod 56primes48.6 %
A142654Primes congruent to 31 mod 56primes48.9 %
A142655Primes congruent to 33 mod 56primes48.7 %
A142656Primes congruent to 37 mod 56primes48.7 %
A142657Primes congruent to 39 mod 56primes48.6 %
A142658Primes congruent to 41 mod 56primes48.4 %
A142659Primes congruent to 43 mod 56primes48.5 %
A142660Primes congruent to 45 mod 56primes48.4 %
A142661Primes congruent to 47 mod 56primes48.7 %
A142662Primes congruent to 51 mod 56primes48.7 %
A142663Primes congruent to 53 mod 56primes48.5 %
A142664Primes congruent to 55 mod 56primes48.2 %
A142665Primes congruent to 1 mod 57primes55.8 %
A142666Primes congruent to 2 mod 57primes55.8 %
A142667Primes congruent to 4 mod 57primes55.8 %
A142668Primes congruent to 5 mod 57primes55.8 %
A142669Primes congruent to 7 mod 57primes55.7 %
A142670Primes congruent to 8 mod 57primes55.9 %
A142671Primes congruent to 10 mod 57primes55.8 %
A142672Primes congruent to 11 mod 57primes56.0 %
A142673Primes congruent to 13 mod 57primes56.0 %
A142674Primes congruent to 14 mod 57primes56.0 %
A142675Primes congruent to 16 mod 57primes55.5 %
A142676Primes congruent to 17 mod 57primes55.9 %
A142677Primes congruent to 20 mod 57primes55.7 %
A142678Primes congruent to 22 mod 57primes55.8 %
A142679Primes congruent to 23 mod 57primes55.9 %
A142680Primes congruent to 25 mod 57primes55.8 %
A142681Primes congruent to 26 mod 57primes55.8 %
A142682Primes congruent to 28 mod 57primes56.0 %
A142683Primes congruent to 29 mod 57primes55.8 %
A142684Primes congruent to 31 mod 57primes56.0 %
A142685Primes congruent to 32 mod 57primes56.1 %
A142686Primes congruent to 34 mod 57primes55.9 %
A142786Primes congruent to 7 mod 60primes52.8 %
A142787Primes congruent to 13 mod 60primes52.8 %
A142788Primes congruent to 17 mod 60primes52.8 %
A142789Primes congruent to 19 mod 60primes52.9 %
A142790Primes congruent to 23 mod 60primes53.0 %
A142791Primes congruent to 29 mod 60primes53.0 %
A142792Primes congruent to 31 mod 60primes52.8 %
A142793Primes congruent to 37 mod 60primes52.9 %
A142794Primes congruent to 41 mod 60primes53.0 %
A142795Primes congruent to 43 mod 60primes52.8 %
A142796Primes congruent to 47 mod 60primes52.7 %
A142797Primes congruent to 49 mod 60primes52.9 %
A142798Primes congruent to 53 mod 60primes52.7 %
A142799Primes congruent to 59 mod 60primes52.6 %
A142889Primes congruent to 1 mod 63primes57.2 %
A142890Primes congruent to 2 mod 63primes57.7 %
A142891Primes congruent to 4 mod 63primes57.4 %
A142892Primes congruent to 5 mod 63primes57.2 %
A142893Primes congruent to 8 mod 63primes57.3 %
A142894Primes congruent to 10 mod 63primes57.2 %
A142895Primes congruent to 11 mod 63primes57.4 %
A142896Primes congruent to 13 mod 63primes57.4 %
A142897Primes congruent to 16 mod 63primes57.4 %
A142898Primes congruent to 17 mod 63primes57.2 %
A142899Primes congruent to 19 mod 63primes57.4 %
A142900Primes congruent to 20 mod 63primes57.3 %
A142901Primes congruent to 22 mod 63primes57.3 %
A142902Primes congruent to 23 mod 63primes57.2 %
A142903Primes congruent to 25 mod 63primes57.3 %
A142904Primes congruent to 26 mod 63primes57.4 %
A142905Primes congruent to 29 mod 63primes57.4 %
A142906Primes congruent to 31 mod 63primes57.4 %
A142907Primes congruent to 32 mod 63primes57.2 %
A142908Primes congruent to 34 mod 63primes57.3 %
A142925Primes congruent to 1 mod 64primes48.0 %
A142926Primes congruent to 3 mod 64primes48.0 %
A142927Primes congruent to 5 mod 64primes48.3 %
A142928Primes congruent to 7 mod 64primes48.1 %
A142929Primes congruent to 9 mod 64primes48.0 %
A142930Primes congruent to 11 mod 64primes47.9 %
A142931Primes congruent to 13 mod 64primes48.2 %
A142932Primes congruent to 15 mod 64primes47.8 %
A142933Primes congruent to 17 mod 64primes48.2 %
A142934Primes congruent to 19 mod 64primes48.0 %
A142935Primes congruent to 23 mod 64primes47.8 %
A142936Primes congruent to 25 mod 64primes47.8 %
A142937Primes congruent to 27 mod 64primes47.8 %
A142938Primes congruent to 29 mod 64primes47.9 %
A142939Primes congruent to 31 mod 64primes48.1 %
A142940Primes congruent to 35 mod 64primes48.0 %
A142941Primes congruent to 37 mod 64primes48.1 %
A142942Primes congruent to 39 mod 64primes47.9 %
A142943Primes congruent to 41 mod 64primes48.0 %
A142944Primes congruent to 43 mod 64primes47.9 %
A142945Primes congruent to 45 mod 64primes48.1 %
A143058a(n) = (n^3 + 18*n^2 + 17*n + 6)/6polynomial100.0 %
A143164Numbers with digitsum 13, in increasing orderdigit rule30.9 %
A143166a(n) = n*(8*n^2 + 1)/3polynomial100.0 %
A143689a(n) = (3*n^2 - n + 2)/2polynomial100.0 %
A143826Numbers k such that 6*k^2 - 1 is primeprime values23.6 %
A143827Numbers k such that 8*k^2 - 1 is primeprime values21.0 %
A143828Primes of the form 10*k^2 - 1primes100.0 %
A143829Numbers n such that 10n^2 - 1 is primeprime values18.8 %
A143831Numbers n such that 12n^2 - 1 is primeprime values19.7 %
A143832Primes of the form 14 n^2-1primes100.0 %
A143833Numbers n such that 14n^2 - 1 is primeprime values24.3 %
A143967Numbers containing only digits 3 or 7 in decimal representationdigit rule18.0 %
A143988Numbers congruent to {5, 13} mod 18residue class26.0 %
A144255Semiprimes of the form k^2+1multiplicative100.0 %
A144312a(n) = 5*n*(5*n + 1)/2polynomial100.0 %
A144314a(n) = 3*n*(6*n + 1)polynomial100.0 %
A144390a(n) = 3*n^2 - n - 1polynomial100.0 %
A144391a(n) = 3*n^2 + n - 1polynomial100.0 %
A144410a(n) = 4*(3*n+1)*(3*n+2)polynomial100.0 %
A144449a(n) = 4*(4 + 9*n^2 + 15*n)polynomial100.0 %
A144459a(n) = (3*n+1)*(5*n+1)polynomial100.0 %
A144555a(n) = 14*n^2polynomial100.0 %
A144571Primes of the form 81n^2 - 90n + 26primes100.0 %
A145018a(n) = (n^2 - n + 8)/2polynomial100.0 %
A145069a(n) = n*(n^2 + 3*n + 5)/3polynomial100.0 %
A145202Primes of form 4*n^2 + 4*n + 653primes100.0 %
A145471Primes p such that (5+p)/2 is primeprimes49.5 %
A145481Primes p such that 2*p - 17 is primeprimes46.7 %
A145482Primes p such that 2*p - 19 is primeprimes47.1 %
A145483Primes p such that 2*p - 23 is primeprimes46.9 %
A145485Primes p such that 2*p - 31 is primeprimes47.3 %
A145486Primes p such that 2*p - 37 is primeprimes47.2 %
A145678a(n) = 441*n^2 - 21polynomial100.0 %
A145749Numbers n such that sigma(n)+phi(n)=sigma(n+1)+phi(n+1)divisor functions47.3 %
A145910a(n) = (1 + 3*n)*(4 + 3*n)/2polynomial100.0 %
A145980a(n) = 29 + 73*n + 37*n^2polynomial100.0 %
A145995a(n) = 8 - 12*n + 5*n^2polynomial100.0 %
A146301a(n) = (8*n+3)*(8*n+7)polynomial100.0 %
A146302a(n) = (8*n+5)*(8*n+9)polynomial100.0 %
A146507Numbers congruent to {1, 13} mod 42residue class39.8 %
A146509Numbers that are congruent to {1, 5} mod 18residue class22.6 %
A146510Numbers congruent to {1, 4} mod 15residue class28.4 %
A146512Numbers congruent to {1, 3} mod 12residue class29.5 %
A147296a(n) = n*(9*n+2)polynomial100.0 %
A147562Number of "ON" cells at n-th stage in the "Ulam-Warburton" two-dimensional cellular automatonself-referential70.9 %
A147874a(n) = (5*n-7)*(n-1)polynomial100.0 %
A147991Sequence S such that 1 is in S and if x is in S, then 3x-1 and 3x+1 are in Sself-referential9.3 %
A151953Primes of the form 6*n^2+17primes100.0 %
A151972Numbers that are congruent to {0, 1, 6, 10} mod 15residue class22.2 %
A151977Numbers that are congruent to {0, 1} mod 16residue class23.0 %
A151978Numbers that are congruent to {0, 1} mod 17residue class20.0 %
A151983Numbers congruent to {0, 1} mod 32residue class25.1 %
A151984Numbers that are congruent to {0, 1} mod 64residue class27.2 %
A152161a(n) = 100*n^2 + 100*n + 21polynomial100.0 %
A152312Primes without odd prime digitsprimes34.1 %
A152313Primes without 0's or primes in their decimal expansionprimes35.6 %
A152470Largest of three consecutive primes whose sum is a primeprimes36.0 %
A152579a(n) = (10*n+3)*(10*n+17)polynomial100.0 %
A152691Multiples of 64residue class9.7 %
A152811a(n) = 2*(n^2 + 2*n - 2)polynomial100.0 %
A152813a(n) = 2*n^2 + 10*n + 3polynomial100.0 %
A152950a(n) = 3 + n*(n-1)/2polynomial100.0 %
A153037a(n) = 2*n^2 + 16*n + 23polynomial100.0 %
A153127a(n) = (2*n + 1)*(5*n + 6)polynomial100.0 %
A153134Numbers k such that 6k - 7 is primeprime values17.4 %
A153135Primes p such that 6*p - 7 is also primeprimes35.4 %
A153145Primes p such that 2*p + 19 is also primeprimes47.4 %
A153169a(n) = 4*n^2 + 12*n + 3polynomial100.0 %
A153183Numbers k such that 3k-2 is primeprime values28.1 %
A153213Primes p such that both p-2 and p+2 are not squarefreeprimes48.5 %
A153218Numbers k such that 6k + 7 is primeprime values17.2 %
A153238Numbers k such that 2*k + 3 is compositecomplement11.5 %
A153355Numbers k such that 5k-1 is a primeprime values21.3 %
A153417Primes p such that p+14 is also primeprimes46.0 %
A153418Primes p such that p+18 is also primeprimes34.9 %
A153419Primes p such that p+20 is also primeprimes44.9 %
A153422Primes of the form k^2 + 15*k + 13primes100.0 %
A153423Primes of the form k^2 + 9*k + 241primes100.0 %
A153502Primes of the form 3*n^2 - 3*n + 11primes100.0 %
A153590Primes p such that p^2 + 3p + 1 is also primeprimes39.9 %
A153591Primes p such that 6p^2+6p+1 is also primeprimes38.7 %
A153642a(n) = 4*n^2 + 24*n + 8polynomial100.0 %
A153644a(n) = 4*n^2 + 28*n + 10polynomial100.0 %
A153762Numbers k such that 8k + 9 is primeprime values16.6 %
A153766Numbers k such that 8k-9 is primeprime values17.1 %
A153767Primes p such that 8*p - 9 is also primeprimes37.8 %
A153781Numbers n such that n^2+13n+23 is primeprime values20.7 %
A153812Primes p such that 6*p^2+1 is also primeprimes49.2 %
A153974Numbers n such that n^3 - 3 is primeprime values23.0 %
A153976a(n) = n^3 + (n+2)^3polynomial100.0 %
A154105a(n) = 12*n^2 + 18*n + 7polynomial100.0 %
A154106a(n) = 12*n^2 + 22*n + 11polynomial100.0 %
A154115Numbers n such that n + 3 is primeprime values16.0 %
A154253Primes of the form 9n^2-8n+2primes100.0 %
A154254a(n) = 9*n^2 - 8*n + 2polynomial100.0 %
A154276Primes of the form 81*k^2 - 72*k + 17primes100.0 %
A154277a(n) = 81*n^2 - 72*n + 17polynomial100.0 %
A154314Numbers with not more than two distinct digits in ternary representationdigit rule11.4 %
A154319Primes p such that p^2 + 2*p - 4 is also primeprimes39.8 %
A154320Primes p such that p^2 + 8*p - 4 is also primeprimes40.2 %
A154357a(n) = 25*n^2 - 14*n + 2polynomial100.0 %
A154359a(n) = 1250*n^2 - 700*n + 99polynomial100.0 %
A154374a(n) = 1250*n^2 - 100*n + 1polynomial100.0 %
A154375a(n) = 1250*n^2 + 100*n + 1polynomial100.0 %
A154376a(n) = 25*n^2 - 2*npolynomial100.0 %
A154377a(n) = 25*n^2 + 2*npolynomial100.0 %
A154405Primes of the form 20n^2+8n+1primes100.0 %
A154409Primes of the form 10n^2+6n+1primes100.0 %
A154414Primes of the form 20*k^2 + 32*k + 13primes100.0 %
A154419Primes of the form 20*k^2 + 36*k + 17primes100.0 %
A154428Primes of the form 50n^2 + 10n + 1primes100.0 %
A154431Primes p such that 5p^2 - p + 1 is primeprimes44.0 %
A154432Numbers k such that 5k^2-k+1 is primeprime values23.1 %
A154514a(n) = 648*n^2 - 72*n + 1polynomial100.0 %
A154515a(n) = 648*n^2 + 72*n + 1polynomial100.0 %
A154516a(n) = 9n^2 - npolynomial100.0 %
A154517a(n) = 9*n^2 + npolynomial100.0 %
A154560a(n) = (n+3)^2*n/2 + 1polynomial100.0 %
A154571Numbers that are congruent to {0, 3, 4, 5, 7, 8} mod 12residue class5.9 %
A154575a(n) = 2*n^2 + 12*n + 4polynomial100.0 %
A154576a(n) = 2*n^2 + 14*n + 5polynomial100.0 %
A154577Primes of the form 2n^2+14n+5primes100.0 %
A154590a(n) = 2*n^2 + 16*n + 6polynomial100.0 %
A154591a(n) = 2*n^2 + 18*n + 7polynomial100.0 %
A154599a(n) = 2*n^2 + 20*n + 8polynomial100.0 %
A154600a(n) = 2*n^2 + 22*n + 9polynomial100.0 %
A154601Primes of the form 2*n^2 + 22*n + 9primes100.0 %
A154607Numbers n such that 11*n + 4 is primeprime values31.1 %
A154608Primes p such that 11*p + 4 is also primeprimes47.2 %
A154610Numbers n such that 13n + 5 is primeprime values21.2 %
A154620Primes p such that 31p+14 is primeprimes46.9 %
A154622Primes p such that 67*p + 32 is also primeprimes48.5 %
A154625Primes p such that 71*p + 34 is also primeprimes48.4 %
A154648Primes of the form n^2 - 13primes100.0 %
A154650Primes p such that 4*p^2-8*p-9 is a primeprimes47.9 %
A154651Numbers k such that 991*k^2+1 is a primeprime values26.0 %
A154761Primes without {1, 9} as digitsprimes32.6 %
A154777Numbers of the form x^2 + 2*y^2 with positive integers x and yquadratic form14.9 %
A155055Primes without positive even digitsprimes27.2 %
A155131Numbers k such that 2^44+k is primeprime values35.8 %
A155152Numbers k such that 13*k^2 + 3*k + 1 is primeprime values20.2 %
A155153Primes p such that 13*p^2+3*p+1 is a primeprimes39.9 %
A155212a(n) = (n^2 + 9*n + 4)/2polynomial100.0 %
A155461a(n) = n^2 + 52*n + 30polynomial100.0 %
A155702Primes of the form 2n^2-9primes100.0 %
A155703Primes p such that 2*p^2 + 16*p + 23 is also primeprimes49.2 %
A155722Numbers k such that 2*k + 9 is primeprime values17.2 %
A155736Numbers n such that 4*n^2+2*n-1 is a primeprime values20.2 %
A155737Primes of the form 4*n^2 + 2*n -1primes100.0 %
A155738Primes p such that 4*p^2+2*p-1 is also primeprimes40.0 %
A155753a(n) = (n^3 - n + 9)/3polynomial100.0 %
A155757a(n) = (n^3 - n + 15)/3polynomial100.0 %
A155771Numbers n such that 2*n^2+2*n-41 is a primeprime values18.5 %
A155772Primes p such that 2*p^2+2*p-41 is a primeprimes37.5 %
A155853Numbers n such that 13*n + 3 is a primeprime values16.2 %
A155937Numbers n such that 13*n + 8 is a primeprime values32.8 %
A155938Primes p such that 13*p + 8 is also primeprimes47.7 %
A155942Numbers k such that 16k+1 is a primeprime values23.4 %
A155943Primes p such that 16*p + 1 is also primeprimes48.3 %
A155965a(n) = n*(n^2+4)polynomial100.0 %
A155966a(n) = 2*n^2 + 8polynomial100.0 %
A156004Primes p such that 8*p+21 is primeprimes36.5 %
A156005Primes p such that 16*p+45 is primeprimes35.0 %
A156007Primes p such that 32*p + 93 is also primeprimes37.7 %
A156009Primes p such that 64*p + 189 is also primeprimes37.1 %
A156104Primes p such that p+36 is also primeprimes36.2 %
A156105Primes p such that p + 72 is also primeprimes36.4 %
A156107Primes p such that p + 144 is also primeprimes36.1 %
A156226Primes of the form 9*n^2 + 1primes100.0 %
A156252Primes of the form 4*n^2+6*n+43primes100.0 %
A156300Primes p such that 4*p - 5 is also primeprimes45.2 %
A156619Numbers congruent to {7, 18} mod 25residue class29.6 %
A156635a(n) = 144*n^2 - npolynomial100.0 %
A156639a(n) = 169*n^2 - 140*n + 29polynomial100.0 %
A156640a(n) = 169*n^2 + 140*n + 29polynomial100.0 %
A156655Primes of the form 1000*k + 1primes71.1 %
A156676a(n) = 81*n^2 - 44*n + 6polynomial100.0 %
A156683Integers that can occur as either leg in more than one primitive Pythagorean triplequadratic form13.7 %
A156711a(n) = 144*n^2 - 161*n + 45polynomial100.0 %
A156719a(n) = 144*n^2 - 127*n + 28polynomial100.0 %
A156721a(n) = 57122*n^2 - 47320*n + 9801polynomial100.0 %
A156735a(n) = 57122*n^2 + 47320*n + 9801polynomial100.0 %
A156774a(n) = 6561*n^2 - 3564*n + 485polynomial100.0 %
A156812a(n) = 225*n^2 - 199*n + 44polynomial100.0 %
A156813a(n) = 225*n^2 - npolynomial100.0 %
A156814a(n) = 225*n^2 + npolynomial100.0 %
A156841a(n) = 529n^2 - 312n + 46polynomial100.0 %
A156842a(n) = 529*n^2 - 746*n + 263polynomial100.0 %
A156843a(n) = 279841n^2 - 165048n + 24335polynomial100.0 %
A156844a(n) = 279841*n^2 - 394634*n + 139128polynomial100.0 %
A156849Numbers k such that k^2 == 2 (mod 23^2)residue class47.4 %
A156853a(n) = 2025*n^2 - 649*n + 52polynomial100.0 %
A156854a(n) = 2025*n^2 - 3401*n + 1428polynomial100.0 %
A156855a(n) = 2025*n^2 - npolynomial100.0 %
A156856a(n) = 2025*n^2 + npolynomial100.0 %
A157010a(n) = 1681*n^2 - 756*n + 85polynomial100.0 %
A157040a(n) = 121*n^2 - 2*npolynomial100.0 %
A157110a(n) = 1681*n^2 - 2606*n + 1010polynomial100.0 %
A157201Numbers k such that 66*k + 1 is primeprime values18.4 %
A157202Numbers k such that 66*k + 5 is primeprime values16.6 %
A157262a(n) = 36*n^2 - 55*n + 21polynomial100.0 %
A157264a(n) = 10368*n^2 - 15840*n + 6049polynomial100.0 %
A157265a(n) = 36*n^2 - 17*n + 2polynomial100.0 %
A157267a(n) = 10368*n^2 - 4896*n + 577polynomial100.0 %
A157286a(n) = 36*n^2 - npolynomial100.0 %
A157288a(n) = 10368*n^2 - 288*n + 1polynomial100.0 %
A157324a(n) = 36*n^2 + npolynomial100.0 %
A157326a(n) = 10368*n^2 + 288*n + 1polynomial100.0 %
A157331a(n) = 128*n^2 - 32*n + 1polynomial100.0 %
A157337a(n) = 128*n^2 + 32*n + 1polynomial100.0 %
A157352Products (semiprimes) of two distinct safe primesmultiplicative50.0 %
A157362a(n) = 49*n^2 - 2*npolynomial100.0 %
A157364a(n) = 4802*n^2 - 196*n + 1polynomial100.0 %
A157365a(n) = 49*n^2 + 2*npolynomial100.0 %
A157367a(n) = 4802*n^2 + 196*n + 1polynomial100.0 %
A157368a(n) = 49*n^2 - 78*n + 31polynomial100.0 %
A157370a(n) = 2401*n^2 - 3822*n + 1520polynomial100.0 %
A157373a(n) = 49*n^2 - 20*n + 2polynomial100.0 %
A157375a(n) = 2401*n^2 - 980*n + 99polynomial100.0 %
A157376a(n) = 6561*n^2 - 7732*n + 2278polynomial100.0 %
A157437Primes congruent to 1, 5, 7, or 11 modulo 24primes28.1 %
A157440a(n) = 121*n^2 - 204*n + 86polynomial100.0 %
A157442a(n) = 14641*n^2 - 24684*n + 10405polynomial100.0 %
A157443a(n) = 121*n^2 - 38*n + 3polynomial100.0 %
A157445a(n) = 14641*n^2 - 4598*n + 362polynomial100.0 %
A157446a(n) = 16*n^2 - npolynomial100.0 %
A157448a(n) = 2048*n^2 - 128*n + 1polynomial100.0 %
A157468Primes of the form sqrt(p-1)-1, where p is a primeprimes42.1 %
A157474a(n) = 16n^2 + npolynomial100.0 %
A157476a(n) = 2048n^2 + 128n + 1polynomial100.0 %
A157483Numbers k such that k-1 and k+1 are divisible by exactly 3 primes, counted with multiplicitymultiplicative22.1 %
A157506a(n) = 13122*n^2 + 324*n + 1polynomial100.0 %
A157507a(n) = 81*n^2 - 2*npolynomial100.0 %
A157509a(n) = 13122*n^2 - 324*n + 1polynomial100.0 %
A157511a(n) = 5000*n^2 + 200*n + 1polynomial100.0 %
A157514a(n) = 25*n^2 - npolynomial100.0 %
A157516a(n) = 5000*n^2 - 200*n + 1polynomial100.0 %
A157610a(n) = 29282*n^2 - 484*n + 1polynomial100.0 %
A157614a(n) = 29282*n^2 + 484*n + 1polynomial100.0 %
A157618a(n) = 625*n^2 - 886*n + 314polynomial100.0 %
A157620a(n) = 781250*n^2 - 1107500*n + 392499polynomial100.0 %
A157621a(n) = 625n^2 - 364n + 53polynomial100.0 %
A157623a(n) = 781250*n^2 - 455000*n + 66249polynomial100.0 %
A157626a(n) = 100*n^2 - 151*n + 57polynomial100.0 %
A157628a(n) = 80000n^2 - 120800n + 45601polynomial100.0 %
A157651a(n) = 100*n^2 - 49*n + 6polynomial100.0 %
A157653a(n) = 80000*n^2 - 39200*n + 4801polynomial100.0 %
A157659a(n) = 100*n^2 - npolynomial100.0 %
A157661a(n) = 80000*n^2 - 800*n + 1polynomial100.0 %
A157664a(n) = 80000*n^2 + 800*n + 1polynomial100.0 %
A157665a(n) = 729*n^2 - 1016*n + 354polynomial100.0 %
A157667a(n) = 531441*n^2 - 740664*n + 258065polynomial100.0 %
A157668a(n) = 729*n^2 - 442*n + 67polynomial100.0 %
A157670a(n) = 531441*n^2 - 322218*n + 48842polynomial100.0 %
A157730a(n) = 441*n^2 - 488*n + 135polynomial100.0 %
A157732a(n) = 388962*n^2 - 430416*n + 119071polynomial100.0 %
A157734a(n) = 441*n^2 - 394*n + 88polynomial100.0 %
A157736a(n) = 388962*n^2 - 347508*n + 77617polynomial100.0 %
A157737a(n) = 441*n^2 - 2*npolynomial100.0 %
A157739a(n) = 388962*n^2 - 1764*n + 1polynomial100.0 %
A157741a(n) = 388962*n^2 + 1764*n + 1polynomial100.0 %
A157757a(n) = 2809*n^2 - 4618*n + 1898polynomial100.0 %
A157760a(n) = 2809*n^2 - 1000*n + 89polynomial100.0 %
A157768a(n) = 27225*n^2 - 39202*n + 14112polynomial100.0 %
A157772Numbers n such that 100n + 13 is primeprime values21.6 %
A157786a(n) = 27225*n^2 - 15248*n + 2135polynomial100.0 %
A157796a(n) = 27225*n^2 - 12098*n + 1344polynomial100.0 %
A157802a(n) = 27225*n^2 - 51302*n + 24168polynomial100.0 %
A157814a(n) = 27225*n^2 - 2*npolynomial100.0 %
A157820a(n) = 27225*n^2 + 2*npolynomial100.0 %
A157824a(n) = 3600*n^2 - 6751*n + 3165polynomial100.0 %
A157838a(n) = 3600*n^2 - 6049*n + 2541polynomial100.0 %
A157842a(n) = 3600*n^2 - 5599*n + 2177polynomial100.0 %
A157853a(n) = 3600*n^2 - 1601*n + 178polynomial100.0 %
A157857a(n) = 3600*n^2 - npolynomial100.0 %
A157861a(n) = 3600*n^2 + npolynomial100.0 %
A157872a(n) = 9*n^2 - 3polynomial100.0 %
A157888a(n) = 81*n^2 + 9polynomial100.0 %
A157889a(n) = 18*n^2 + 1polynomial100.0 %
A157909a(n) = 81*n^2 - 9polynomial100.0 %
A157910a(n) = 18*n^2 - 1polynomial100.0 %
A157912a(n) = 64*n^2 + 16polynomial100.0 %
A157913a(n) = 64*n^2 - 16polynomial100.0 %
A157914a(n) = 8*n^2 - 1polynomial100.0 %
A157915a(n) = 625*n^2 + 25polynomial100.0 %
A157916a(n) = 50*n^2 + 1polynomial100.0 %
A157918a(n) = 625*n^2 - 25polynomial100.0 %
A157919a(n) = 50*n^2 - 1polynomial100.0 %
A157923a(n) = 49*n^2 - npolynomial100.0 %
A157931Numbers that are both the sum and the product of two primesmultiplicative21.8 %
A157948a(n) = 64*n^2 - npolynomial100.0 %
A157953a(n) = 81n^2 - npolynomial100.0 %
A157960a(n) = 121*n^2 - npolynomial100.0 %
A157974Primes p such that 12*p + 11 is also primeprimes36.5 %
A157975Primes p such that 16*p + 15 is also primeprimes35.2 %
A157976Primes p such that 18*p + 17 is also primeprimes36.8 %
A157977Primes p such that 20*p + 19 is also primeprimes45.7 %
A157978Primes p such that 4*p - 3 is also a primeprimes37.0 %
A157998a(n) = 169*n^2 - npolynomial100.0 %
A158003a(n) = 196*n^2 - npolynomial100.0 %
A158010a(n) = 256*n^2 - npolynomial100.0 %
A158015Primes p such that 6*p-1 is also primeprimes37.3 %
A158016Primes p such that 8*p-1 is also primeprimes47.8 %
A158017Primes p such that 10*p-1 is also primeprimes46.1 %
A158056a(n) = 16*n^2 + 2*npolynomial100.0 %
A158058a(n) = 16*n^2 - 2*npolynomial100.0 %
A158062a(n) = 36*n^2 - 2*npolynomial100.0 %
A158064a(n) = 36*n^2 + 2*npolynomial100.0 %
A158067a(n) = 64*n^2 - 2*npolynomial100.0 %
A158070a(n) = 64*n^2 + 2*npolynomial100.0 %
A158127a(n) = 100*n^2 + 2*npolynomial100.0 %
A158129a(n) = 100*n^2 - 2*npolynomial100.0 %
A158132a(n) = 144n^2 + 2npolynomial100.0 %
A158135a(n) = 144*n^2 - 2*npolynomial100.0 %
A158186a(n) = 10*n^2 - 7*n + 1polynomial100.0 %
A158187a(n) = 10*n^2 + 1polynomial100.0 %
A158218a(n) = 169*n^2 - 2*npolynomial100.0 %
A158220a(n) = 169*n^2 + 2*npolynomial100.0 %
A158222a(n) = 196*n^2 + 2*npolynomial100.0 %
A158224a(n) = 196*n^2 - 2*npolynomial100.0 %
A158226a(n) = 225*n^2 - 2*npolynomial100.0 %
A158228a(n) = 225n^2 + 2npolynomial100.0 %
A158230a(n) = 256*n^2 + 2*npolynomial100.0 %
A158249a(n) = 256*n^2 - 2*npolynomial100.0 %
A158252a(n) = 289*n^2 - 2*npolynomial100.0 %
A158254a(n) = 289n^2 + 2npolynomial100.0 %
A158271a(n) = 324n^2 + 2npolynomial100.0 %
A158305a(n) = 324n^2 - 2npolynomial100.0 %
A158307a(n) = 361*n^2 - 2*npolynomial100.0 %
A158309a(n) = 361*n^2 + 2*npolynomial100.0 %
A158312a(n) = 400*n^2 + 2*npolynomial100.0 %
A158316a(n) = 400*n^2 - 2*npolynomial100.0 %
A158318Primes p such that 5p-2 is primeprimes45.7 %
A158321a(n) = 441n^2 + 2npolynomial100.0 %
A158325a(n) = 484*n^2 + 2*npolynomial100.0 %
A158329a(n) = 484*n^2 - 2*npolynomial100.0 %
A158364a(n) = 529*n^2 - 2*npolynomial100.0 %
A158367a(n) = 529*n^2 + 2*npolynomial100.0 %
A158369a(n) = 576*n^2 + 2*npolynomial100.0 %
A158371a(n) = 576*n^2 - 2*npolynomial100.0 %
A158373a(n) = 625*n^2 - 2*npolynomial100.0 %
A158382a(n) = 625*n^2 + 2*npolynomial100.0 %
A158385a(n) = 676*n^2 + 2*npolynomial100.0 %
A158392a(n) = 676*n^2 - 2*npolynomial100.0 %
A158394a(n) = 729*n^2 - 2*npolynomial100.0 %
A158396a(n) = 729*n^2 + 2*npolynomial100.0 %
A158398a(n) = 784*n^2 - 2*npolynomial100.0 %
A158401a(n) = 841*n^2 - 2*npolynomial100.0 %
A158403a(n) = 841*n^2 + 2*npolynomial100.0 %
A158406a(n) = 900*n^2 + 2*npolynomial100.0 %
A158408a(n) = 900*n^2 - 2*npolynomial100.0 %
A158410a(n) = 961*n^2 - 2*npolynomial100.0 %
A158413a(n) = 961*n^2 + 2*npolynomial100.0 %
A158420a(n) = 1024*n^2 - 2*npolynomial100.0 %
A158443a(n) = 16*n^2 - 4polynomial100.0 %
A158444a(n) = 16*n^2 + 4polynomial100.0 %
A158445a(n) = 25*n^2 + 5polynomial100.0 %
A158446a(n) = 25*n^2 - 5polynomial100.0 %
A158447a(n) = 10*n^2 - 1polynomial100.0 %
A158462a(n) = 36*n^2 - 6polynomial100.0 %
A158479a(n) = 36*n^2 + 6polynomial100.0 %
A158480a(n) = 12*n^2 + 1polynomial100.0 %
A158481a(n) = 49*n^2 + 7polynomial100.0 %
A158482a(n) = 14*n^2 + 1polynomial100.0 %
A158484a(n) = 49*n^2 - 7polynomial100.0 %
A158485a(n) = 14*n^2 - 1polynomial100.0 %
A158487a(n) = 64*n^2 - 8polynomial100.0 %
A158488a(n) = 64*n^2 + 8polynomial100.0 %
A158490a(n) = 100*n^2 - 10polynomial100.0 %
A158491a(n) = 20*n^2 - 1polynomial100.0 %
A158492a(n) = 100*n^2 + 10polynomial100.0 %
A158493a(n) = 20*n^2 + 1polynomial100.0 %
A158536a(n) = 121*n^2 + 11polynomial100.0 %
A158537a(n) = 22*n^2 + 1polynomial100.0 %
A158539a(n) = 121*n^2 - 11polynomial100.0 %
A158540a(n) = 22*n^2 - 1polynomial100.0 %
A158543a(n) = 144*n^2 - 12polynomial100.0 %
A158544a(n) = 24*n^2 - 1polynomial100.0 %
A158546a(n) = 144*n^2 + 12polynomial100.0 %
A158547a(n) = 24*n^2 + 1polynomial100.0 %
A158548a(n) = 169*n^2 + 13polynomial100.0 %
A158549a(n) = 26*n^2 + 1polynomial100.0 %
A158550a(n) = 169*n^2 - 13polynomial100.0 %
A158551a(n) = 26*n^2 - 1polynomial100.0 %
A158553a(n) = 196*n^2 - 14polynomial100.0 %
A158554a(n) = 28*n^2 - 1polynomial100.0 %
A158555a(n) = 196*n^2 + 14polynomial100.0 %
A158556a(n) = 28*n^2 + 1polynomial100.0 %
A158557a(n) = 225*n^2 + 15polynomial100.0 %
A158558a(n) = 30*n^2 + 1polynomial100.0 %
A158559a(n) = 225*n^2 - 15polynomial100.0 %
A158560a(n) = 30*n^2 - 1polynomial100.0 %
A158562a(n) = 256*n^2 - 16polynomial100.0 %
A158563a(n) = 32*n^2 - 1polynomial100.0 %
A158573Numbers k such that 30*k + 7 is primeprime values16.4 %
A158574a(n) = 256*n^2 + 16polynomial100.0 %
A158575a(n) = 32*n^2 + 1polynomial100.0 %
A158585a(n) = 289*n^2 + 17polynomial100.0 %
A158586a(n) = 34*n^2 + 1polynomial100.0 %
A158587a(n) = 289*n^2 - 17polynomial100.0 %
A158588a(n) = 34*n^2 - 1polynomial100.0 %
A158589a(n) = 324*n^2 - 18polynomial100.0 %
A158590a(n) = 324*n^2 + 18polynomial100.0 %
A158591a(n) = 36*n^2 + 1polynomial100.0 %
A158592a(n) = 361*n^2 + 19polynomial100.0 %
A158593a(n) = 38*n^2 + 1polynomial100.0 %
A158595a(n) = 361*n^2 - 19polynomial100.0 %
A158596a(n) = 38*n^2 - 1polynomial100.0 %
A158597a(n) = 400*n^2 - 20polynomial100.0 %
A158598a(n) = 40*n^2 - 1polynomial100.0 %
A158601a(n) = 400*n^2 + 20polynomial100.0 %
A158602a(n) = 40*n^2 + 1polynomial100.0 %
A158603a(n) = 441*n^2 + 21polynomial100.0 %
A158604a(n) = 42*n^2 + 1polynomial100.0 %
A158614Numbers n such that 30*n + 11 is primeprime values15.9 %
A158626a(n) = 42*n^2 - 1polynomial100.0 %
A158627a(n) = 484*n^2 - 22polynomial100.0 %
A158628a(n) = 44*n^2 - 1polynomial100.0 %
A158629a(n) = 484*n^2 + 22polynomial100.0 %
A158630a(n) = 44*n^2 + 1polynomial100.0 %
A158631a(n) = 529*n^2 + 23polynomial100.0 %
A158632a(n) = 46*n^2 + 1polynomial100.0 %
A158633a(n) = 529*n^2 - 23polynomial100.0 %
A158634a(n) = 46*n^2 - 1polynomial100.0 %
A158636a(n) = 576*n^2 - 24polynomial100.0 %
A158637a(n) = 576*n^2 + 24polynomial100.0 %
A158638a(n) = 48*n^2 + 1polynomial100.0 %
A158639a(n) = 676*n^2 - 26polynomial100.0 %
A158640a(n) = 52*n^2 - 1polynomial100.0 %
A158643a(n) = 676*n^2 + 26polynomial100.0 %
A158644a(n) = 52*n^2 + 1polynomial100.0 %
A158645a(n) = 729*n^2 + 27polynomial100.0 %
A158646a(n) = 54*n^2 + 1polynomial100.0 %
A158648Numbers n such that 30*n + 17 is primeprime values17.3 %
A158655a(n) = 729*n^2 - 27polynomial100.0 %
A158656a(n) = 54*n^2 - 1polynomial100.0 %
A158657a(n) = 784*n^2 - 28polynomial100.0 %
A158658a(n) = 56*n^2 - 1polynomial100.0 %
A158659a(n) = 784*n^2 + 28polynomial100.0 %
A158660a(n) = 56*n^2 + 1polynomial100.0 %
A158665a(n) = 841*n^2 + 29polynomial100.0 %
A158666a(n) = 58*n^2 + 1polynomial100.0 %
A158667a(n) = 841*n^2 - 29polynomial100.0 %
A158668a(n) = 58*n^2 - 1polynomial100.0 %
A158669a(n) = 900*n^2 - 30polynomial100.0 %
A158670a(n) = 60*n^2 - 1polynomial100.0 %
A158672a(n) = 900*n^2 + 30polynomial100.0 %
A158673a(n) = 60*n^2 + 1polynomial100.0 %
A158675a(n) = 961*n^2 + 31polynomial100.0 %
A158676a(n) = 62*n^2 + 1polynomial100.0 %
A158679a(n) = 961*n^2 - 31polynomial100.0 %
A158680a(n) = 62*n^2 - 1polynomial100.0 %
A158683a(n) = 1024*n^2 - 32polynomial100.0 %
A158684a(n) = 64*n^2 - 1polynomial100.0 %
A158685a(n) = 32*(32*n^2 + 1)polynomial100.0 %
A158686a(n) = 64*n^2 + 1polynomial100.0 %
A158688a(n) = 1089*n^2 + 33polynomial100.0 %
A158689a(n) = 66*n^2 + 1polynomial100.0 %
A158692a(n) = 1089*n^2 - 33polynomial100.0 %
A158693a(n) = 66*n^2 - 1polynomial100.0 %
A158704Nonnegative integers with an even number of even powers of 2 in their base-2 representationdigit rule15.3 %
A158705Nonnegative integers with an odd number of even powers of 2 in their base-2 representationdigit rule15.0 %
A158714Primes p such that p1 = ceiling(p/2) + p is prime and p2 = floor(p1/2) + p1 is primeprimes65.8 %
A158729a(n) = 1156*n^2 - 34polynomial100.0 %
A158730a(n) = 68*n^2 - 1polynomial100.0 %
A158731a(n) = 1156*n^2 + 34polynomial100.0 %
A158732a(n) = 68*n^2 + 1polynomial100.0 %
A158733a(n) = 1225*n^2 + 35polynomial100.0 %
A158734a(n) = 70*n^2 + 1polynomial100.0 %
A158735a(n) = 1225*n^2 - 35polynomial100.0 %
A158736a(n) = 70*n^2 - 1polynomial100.0 %
A158737a(n) = 1296*n^2 - 36polynomial100.0 %
A158738a(n) = 72*n^2 - 1polynomial100.0 %
A158739a(n) = 1296*n^2 + 36polynomial100.0 %
A158740a(n) = 72*n^2 + 1polynomial100.0 %
A158741a(n) = 1369*n^2 + 37polynomial100.0 %
A158742a(n) = 74*n^2 + 1polynomial100.0 %
A158743a(n) = 1369*n^2 - 37polynomial100.0 %
A158744a(n) = 74*n^2 - 1polynomial100.0 %
A158746Numbers n such that 30*n + 13 is primeprime values16.9 %
A158764a(n) = 38*(38*n^2 - 1)polynomial100.0 %
A158765a(n) = 76*n^2 - 1polynomial100.0 %
A158766a(n) = 1444*n^2 + 38polynomial100.0 %
A158767a(n) = 76*n^2 + 1polynomial100.0 %
A158768a(n) = 1521*n^2 + 39polynomial100.0 %
A158769a(n) = 78*n^2 + 1polynomial100.0 %
A158770a(n) = 1521*n^2 - 39polynomial100.0 %
A158771a(n) = 78*n^2 - 1polynomial100.0 %
A158773a(n) = 1600*n^2 - 40polynomial100.0 %
A158774a(n) = 80*n^2 - 1polynomial100.0 %
A158775a(n) = 1600*n^2 + 40polynomial100.0 %
A158776a(n) = 80*n^2 + 1polynomial100.0 %
A158791Numbers n such that 30*n + 23 is primeprime values17.1 %
A158806Numbers n such that 30*n + 19 is primeprime values16.6 %
A158850Numbers k such that 30*k + 29 is primeprime values16.9 %
A160545Numbers coprime to 21residue class4.1 %
A160548Primes of the form k^2 + k + 844427primes99.9 %
A160591Indices of primes congruent to 5 modulo 12primes16.7 %
A160749a(n) = (11*n^2 + 19*n + 10)/2polynomial100.0 %
A160805a(n) = (2*n^3 + 9*n^2 + n + 24) / 6polynomial100.0 %
A160950Primes p such that 2p + 105 is primeprimes33.0 %
A160951Primes p such that 2p + 1155 is primeprimes31.6 %
A161008Primes of the form 2*k^2 + 5939831primes99.9 %
A161504Primes congruent to {1, 2, 10, 11, 19, 20} mod 21primes27.9 %
A161505Primes congruent to {1, 7, 8, 25, 26, 32} mod 33primes32.6 %
A161532a(n) = 2*n^2 + 8*n + 1polynomial100.0 %
A161549a(n) = 2*n^2 + 14*n + 1polynomial100.0 %
A161587a(n) = 13*n^2 + 10*n + 1polynomial100.0 %
A161613Primes p such that 2p+3*5*7*11*13*17*19*23*29*31*37 is primeprimes34.2 %
A161616Primes p such that 2*p+111546435 is also primeprimes31.6 %
A161617a(n) = 8*n^2 + 20*n + 1polynomial100.0 %
A161703a(n) = (4*n^3 - 12*n^2 + 14*n + 3)/3polynomial100.0 %
A161707a(n) = (4*n^3 - 9*n^2 + 11*n + 3)/3polynomial100.0 %
A161712a(n) = (4*n^3 - 6*n^2 + 8*n + 3)/3polynomial100.0 %
A162147a(n) = n*(n+1)*(5*n + 4)/6polynomial100.0 %
A162148a(n) = n*(n+1)*(5*n+7)/6polynomial100.0 %
A162174Primes classified by levelprimes51.6 %
A162175Primes classified by weightprimes7.5 %
A162254a(n) = n*(2*n^2 + 5*n + 1)/2polynomial100.0 %
A162256a(n) = (2*n^3 + 5*n^2 - 3*n)/2polynomial100.0 %
A162260a(n) = (n^3 + 4*n^2 - n)/2polynomial100.0 %
A162261a(n) = (2*n^3 + 5*n^2 - 7*n)/2polynomial100.0 %
A162263a(n) = (2*n^3 + 5*n^2 + 11*n)/2polynomial100.0 %
A162264a(n) = (2*n^3 + 5*n^2 + 7*n)/2polynomial100.0 %
A162265a(n) = (2*n^3 + 5*n^2 - 5*n)/2polynomial100.0 %
A162266a(n) = (2*n^3 + 5*n^2 + 21*n)/2polynomial100.0 %
A162267a(n) = (2*n^3 + 5*n^2 + 5*n)/2polynomial100.0 %
A162316a(n) = 5*n^2 + 20*n + 1polynomial100.0 %
A162527Numbers k whose largest divisor <= sqrt(k) equals 7divisor functions23.1 %
A162540a(n) = (2*n+1)*(2*n+3)*(2*n+5)/3polynomial100.0 %
A162860Numbers k such that k^2+4*k+1 is primeprime values23.8 %
A163303a(n) = n^3 + 73*n^2 + n + 67polynomial100.0 %
A163612Primes of form 5207*n + 1primes89.1 %
A163623Primes of the form 120*k + 1primes57.1 %
A163624Numbers k such that 120*k+1 is primeprime values17.6 %
A163627Numbers k such that 42k + 5 is primeprime values15.7 %
A163655a(n) = n*(2*n^2 + 5*n + 13)/2polynomial100.0 %
A163661a(n) = n*(2*n^2 + 5*n + 17)/2polynomial100.0 %
A163673a(n) = n*(2*n^2 + 5*n + 15)/2polynomial100.0 %
A163675a(n) = n*(2*n^2 + 5*n + 19)/2polynomial100.0 %
A163683a(n) = n^2*(2*n + 5)polynomial100.0 %
A163758a(n) = 9*n*(n+1)polynomial100.0 %
A163761a(n) = 10*n*(n+1)polynomial100.0 %
A163815a(n) = n*(2*n^2 + 5*n + 3)polynomial100.0 %
A163832a(n) = n*(2*n^2 + 5*n + 1)polynomial100.0 %
A163833a(n) = n*(6*n^2 + 15*n + 5)/2polynomial100.0 %
A164042Primes p such that 2*p^2+4*p+1 is also primeprimes38.8 %
A164136a(n) = 11*n*(n+1)polynomial100.0 %
A164845a(n) = (6 + 10*n + 5*n^2 + n^3)/2polynomial100.0 %
A164897a(n) = 4*n*(n+1) + 3polynomial100.0 %
A165682Primes p such that 3*p*(p-1)+1 is also primeprimes41.1 %
A165798a(n) = 65*n^2polynomial100.0 %
A165806a(n) = 15n^2 + 3n + 1polynomial100.0 %
A165810Primes p such that 18*p+1 is also a primeprimes38.2 %
A166005Primes p such that 8*p+15 is also a primeprimes35.1 %
A166136a(n) = n*(n+3)/2 + 7polynomial100.0 %
A166137a(n) = 5*n*(n+1)/2 - 4polynomial100.0 %
A166143a(n) = 3*n^2 + 3*n - 5polynomial100.0 %
A166144a(n) = (11*n^2 + 11*n - 20)/2polynomial100.0 %
A166146a(n) = (7*n^2 + 7*n - 12)/2polynomial100.0 %
A166147a(n) = 4*n^2 + 4*n - 7polynomial100.0 %
A166148a(n) = (9*n^2 + 9*n - 16)/2polynomial100.0 %
A166150a(n) = 5*n^2 + 5*n - 9polynomial100.0 %
A166151a(n) = (5*n^2 + 5*n - 6)/2polynomial100.0 %
A166154a(n) = 7*n*(n+1)/2 - 5polynomial100.0 %
A166457Numbers n such that n*100+1 is primeprime values22.1 %
A166464a(n) = (3 + 2*n + 6*n^2 + 4*n^3)/3polynomial100.0 %
A166547Primes of the form 100*k+7primes52.8 %
A166560Primes of the form 100*n+9primes53.2 %
A166573Prime numbers containing the string 13primes29.7 %
A166911a(n) = (9 + 14*n + 12*n^2 + 4*n^3)/3polynomial100.0 %
A167055Numbers k such that 12*k + 5 is primeprime values16.5 %
A167056Numbers k such that 12*k + 7 is primeprime values17.4 %
A167057Numbers k such that 12*k + 11 is primeprime values18.3 %
A167119Primes congruent to 2, 3, 5, 7 or 11 (mod 13)primes31.5 %
A167134Primes congruent to {2, 3, 5, 7} mod 11primes30.7 %
A167135Primes congruent to {2, 3, 5, 7, 11} mod 12primes26.2 %
A167469a(n) = 3*n*(5*n-1)/2polynomial100.0 %
A167487a(n) = n*(n + 3)/2 + 8polynomial100.0 %
A167499a(n) = n*(n+3)/2 + 6polynomial100.0 %
A167573a(n) = 20*n^2 + 3polynomial100.0 %
A167585a(n) = 12*n^2 - 8*n + 9polynomial100.0 %
A168235a(n) = 1+5*n+7*n^2polynomial100.0 %
A168240a(n) = 13*n^2 + 7*n + 1polynomial100.0 %
A168484Numbers that are congruent to {2, 3, 5, 7} mod 11residue class16.0 %
A168486Numbers that are congruent to {2, 5} mod 11residue class21.9 %
A168489Numbers that are congruent to {7,11} mod 12residue class18.0 %
A168501Numbers without the decimal digits 2, 4 and 6digit rule16.1 %
A168547a(n) = 1 - 2*n^2 + 4*n*(1 + 2*n^2)/3polynomial100.0 %
A168574a(n) = (4*n + 3)*(1 + 2*n^2)/3polynomial100.0 %
A168668a(n) = n*(2 + 5*n)polynomial100.0 %
A168670Numbers that are congruent to {1, 8} mod 11residue class22.4 %
A168671Numbers that are congruent to {1, 10} mod 13residue class23.1 %
A168672Numbers that are congruent to {2,13} mod 17residue class24.9 %
A169597Numbers that are congruent to {2, 15} mod 19residue class25.4 %
A169598Numbers that are congruent to {3,18} mod 23residue class26.7 %
A169599Numbers that are congruent to {4, 23} mod 29residue class28.1 %
A169600Numbers that are congruent to {4, 25} mod 31residue class28.3 %
A169610Numbers that are congruent to {5, 30} mod 37residue class29.5 %
A169823Multiples of 60residue class9.7 %
A171139Primes p such that 7*p^2+7*p-1 is also primeprimes39.7 %
A171141Numbers that are congruent to {6,33} mod 41residue class30.2 %
A171272a(n) = 1 + 4*n*(1 + 2*n^2)/3polynomial100.0 %
A171409Primes p such that 9014*p+1 is also primeprimes50.0 %
A171517Primes p such that 2*p+11 is primeprimes46.7 %
A171748Primes of the form (2+n)*(1+2*n)+(1+n)*(2+2*n)primes100.0 %
A171838Primes of the form 3*k^2 + 9*k + 5primes100.0 %
A172043a(n) = 5*n^2 - n + 1polynomial100.0 %
A172044a(n) = 5*n^2 + 11*n + 1polynomial100.0 %
A172073a(n) = (4*n^3 + n^2 - 3*n)/2polynomial100.0 %
A172076a(n) = n*(n+1)*(14*n-11)/6polynomial100.0 %
A172078a(n) = n*(16*n^2 + 3*n - 13)/6polynomial100.0 %
A172082a(n) = n*(n+1)*(6*n-5)/2polynomial100.0 %
A172117a(n) = n*(n+1)*(20*n-17)/6polynomial100.0 %
A172122Primes p such that 7*p^2+7*p+1 is also primeprimes52.0 %
A172193a(n) = 5*n^2 + 31*n + 1polynomial100.0 %
A172443Numbers with exactly 64 divisorsmultiplicative27.1 %
A172469Primes congruent to +/-1 or +/-7 modulo 25primes35.5 %
A172482a(n) = (1+n)*(9 + 11*n + 4*n^2)/3polynomial100.0 %
A172981Primes p such that 210*p+41 is also primeprimes34.8 %
A173089a(n) = 25*n^2 + npolynomial100.0 %
A173141a(n) = 49*n^2 + npolynomial100.0 %
A173267a(n) = 121*n^2 + npolynomial100.0 %
A173274Primes of the form x^2 + 18480*y^2quadratic form68.5 %
A173275a(n) = 169*n^2 + npolynomial100.0 %
A173307a(n) = 13*n*(n+1)polynomial100.0 %
A173308a(n) = 17*n*(n+1)polynomial100.0 %
A173309a(n) = 19*n*(n+1)polynomial100.0 %
A173552Numbers k such that 5+38*k^2 is a primeprime values16.4 %
A173554Primes of form 5+38*n^2primes100.0 %
A173555Primes p such that 5+38*p^2 is also primeprimes35.0 %
A173580Primes where each digit is 0, 1, 2, 4, or 8primes40.4 %
A173626Primes p such that p-1 has no prime factors larger than sqrt(p)primes31.4 %
A174138Numbers congruent to {5,6,7,8,9,15,16,17,18,19} mod 25residue class12.5 %
A174139Numbers congruent to {0,1,2,3,4,10,11,12,13,14,20,21,22,23,24} mod 25residue class11.3 %
A174152Primes p such that p^2+p+9 is also primeprimes52.7 %
A174281Primes p such that 20*p^2+32*p+13 is also primeprimes39.5 %
A174333a(n) = 61*n^2polynomial100.0 %
A174334a(n) = 73*n^2polynomial100.0 %
A174337a(n) = 94*n^2polynomial100.0 %
A174338a(n) = 97*n^2polynomial100.0 %
A174339a(n) = 109*n^2polynomial100.0 %
A174396Numbers congruent to {1,4,5,8} mod 9residue class10.2 %
A174398Numbers that are congruent to {1, 4, 5, 8} mod 12residue class18.6 %
A174438Numbers that are congruent to {0, 2, 5, 8} mod 9residue class18.6 %
A174635Prime numbers that are not Ramanujan primesprimes28.4 %
A174723a(n) = n*(4*n^2 - 3*n + 5)/6polynomial100.0 %
A174812Primes of the form n^2+42primes100.0 %
A174813a(n) = number whose product of digits equals a power of 3digit rule20.4 %
A174814a(n) = n*(n+1)*(5*n+1)/3polynomial100.0 %
A174905Numbers with no pair (d,e) of divisors such that d < e < 2*ddivisor functions8.6 %
A174913Lesser of twin primes p1 and p2 such that 2*p1+p2 is a prime numberprimes64.1 %
A175063Primes p such that 5*p^2 + 5*p + 1 is also primeprimes38.0 %
A175461Semiprimes of form 8n+5multiplicative30.9 %
A175463Numbers k such that 8*k + 5 is semiprimemultiplicative15.9 %
A175495Positive integers k such that k < 2^d(k), where d(k) is the number of divisors of kdivisor functions16.6 %
A175648Semiprimes m such that m+4 is also semiprimemultiplicative26.8 %
A175742Numbers with 32 divisorsmultiplicative23.8 %
A175746Numbers with 36 divisorsmultiplicative27.9 %
A175749Numbers with 40 divisorsmultiplicative27.9 %
A175750Numbers with 42 divisorsmultiplicative40.9 %
A175754Numbers with 48 divisorsmultiplicative22.5 %
A175884Numbers that are congruent to {0, 2, 4, 7, 9} mod 12residue class16.2 %
A175885Numbers that are congruent to {1, 10} mod 11residue class20.8 %
A175886Numbers that are congruent to {1, 12} mod 13residue class21.3 %
A175887Numbers that are congruent to {1, 14} mod 15residue class12.1 %
A176547Numbers n such that 2*n^2 + 6*n + 1 is primeprime values19.1 %
A176549Primes of the form 2*n^2+6*n+1primes100.0 %
A176617Primes of the form 14*k^2 + 26*k + 13primes100.0 %
A176783Primes of the form 13*n^2+3*n+1primes100.0 %
A176969Numbers n such that n^2 + 13^2 is primeprime values23.2 %
A176995Numbers that can be written as (m + sum of digits of m) for some mdigit rule10.0 %
A177059a(n) = 25*n^2 + 25*n + 6polynomial100.0 %
A177065a(n) = (8*n+3)*(8*n+5)polynomial100.0 %
A177071a(n) = (7*n + 3)*(7*n + 4)polynomial100.0 %
A177072a(n) = (9*n+2)*(9*n+7)polynomial100.0 %
A177073a(n) = (9*n+4)*(9*n+5)polynomial100.0 %
A177092Primes p such that 11*p + 2 is also primeprimes47.5 %
A177099a(n) = 81*n^2 + 2*npolynomial100.0 %
A177342a(n) = (4*n^3-3*n^2+5*n-3)/3polynomial100.0 %
A178361Numbers with rounded up arithmetic mean of digits = 1digit rule13.8 %
A178403Numbers containing the rounded up arithmetic mean of their digits at least once, cf. A004427digit rule11.7 %
A178574a(n) = 2*n*(9*n-1)polynomial100.0 %
A178977a(n) = (3*n+2)*(3*n+5)/2polynomial100.0 %
A179188Numbers n such that phi(n) = phi(n+6), with Euler's totient function phi=A000010divisor functions38.0 %
A179231Primes of the form 250n + 1primes59.4 %
A179244Numbers that have 4 terms in their Zeckendorf representationdigit rule27.9 %
A179336Primes containing at least one prime digit in base 10primes23.3 %
A179436a(n) = (3*n+7)*(3*n+2)/2polynomial100.0 %
A180223a(n) = (11*n^2 - 7*n)/2polynomial100.0 %
A180232a(n) = n*(17*n - 13)/2polynomial100.0 %
A180415a(n) = (n^3 - 3n^2 + 14n - 6)/6polynomial100.0 %
A180748Numbers k such that k^2 - k + 1 is semiprimemultiplicative16.7 %
A180919a(n) = n^2 + 731*n + 1polynomial100.0 %
A180923Numbers n such that 111*n + 1 is primeprime values19.4 %
A180939Numbers n such that n^2 - 2999n + 2248541 is primeprime values15.7 %
A180948Smallest of seven (7) consecutive primes whose sum is a primeprimes38.4 %
A180950Smallest prime such that the sum of successive 11 primes is a primeprimes38.7 %
A181679a(n) = 121*n^2 + 2*npolynomial100.0 %
A181732Numbers n such that 90n + 1 is primeprime values17.5 %
A181780Numbers n which are Fermat pseudoprimes to some base b, 2 <= b <= n-2primes10.5 %
A181890a(n) = 8*n^2 + 14*n + 5polynomial100.0 %
A182175Numbers with the property that every pair of adjacent digits sum to a prime numberdigit rule14.5 %
A182760Beatty sequence for (3 + 5^(-1/2))/2Beatty12.6 %
A184618a(n) = floor(n*r + h), where r=sqrt(2) and h=1/3; complement of A184619Beatty11.3 %
A184774Primes of the form floor(k*sqrt(2))Beatty25.8 %
A185019a(n) = n*(14*n-3)polynomial100.0 %
A185022Prime p such that p, p+12, p+24 are all primesprimes48.8 %
A185086Fouvry-Iwaniec primes: Primes of the form k^2 + p^2 where p is a primeprimes37.7 %
A185212a(n) = 12*n^2 - 8*n + 1polynomial100.0 %
A185438a(n) = 8*n^2 - 2*n + 1polynomial100.0 %
A185669a(n) = 4*n^2 + 3*n + 2polynomial100.0 %
A185939a(n) = 9*n^2 - 6*n + 2polynomial100.0 %
A186029a(n) = n*(7*n+3)/2polynomial100.0 %
A186030a(n) = n*(13*n-3)/2polynomial100.0 %
A186525Semiprimes of the form 7k+1multiplicative32.4 %
A186815Numbers n such that n^2-10 is a primeprime values28.0 %
A187710a(n) = n^2 + n + 10polynomial100.0 %
A188135a(n) = 8*n^2 + 2*n + 1polynomial100.0 %
A188377a(n) = n^3 - 4*n^2 + 6*n - 2polynomial100.0 %
A188382Primes of the form 8*n^2 + 2*n + 1primes100.0 %
A188459Numbers k such that 4*k^2 + 4*k + 653 is a primeprime values16.0 %
A188475a(n) = (2*n^3 + 3*n^2 + n + 3)/3polynomial100.0 %
A188549Numbers k such that 8*k^2+1 is a primeprime values19.7 %
A188947a(n) = n^3 - 2*n^2 + 2*n + 1polynomial100.0 %
A189833a(n) = n^2 + 8polynomial100.0 %
A189834a(n) = n^2 + 9polynomial100.0 %
A189836a(n) = n^2 + 11polynomial100.0 %
A189890a(n) = (n^3 - 2*n^2 + 3*n + 2)/2polynomial100.0 %
A190576a(n) = n^2 + 5*n - 5polynomial100.0 %
A190719Numbers that are congruent to {0, 1, 3, 5, 7, 8, 11} mod 12residue class15.6 %
A190785Numbers that are congruent to {0, 2, 3, 5, 7, 9, 11} mod 12residue class19.8 %
A190803Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x-1 and 3x-1 are in aself-referential26.3 %
A190898Least odd prime p>n^2 with (n/p) = 1, where ( / ) is the Legendre symbolprimes100.0 %
A191021Primes that are squares mod 23primes27.1 %
A191022Primes that are squares mod 29primes29.3 %
A191024Primes that are squares mod 31primes27.8 %
A191027Primes that are nonzero squares mod 37primes29.0 %
A191060Primes that are not squares mod 11primes30.5 %
A191063Primes that are not squares mod 19primes29.7 %
A191065Primes that are not squares mod 23primes28.1 %
A191067Primes that are not squares mod 31primes27.7 %
A191073Primes that are not squares mod 51primes28.3 %
A191113Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x-2 and 4x-2 are in aself-referential21.9 %
A191275Numbers that are congruent to {0, 1, 3, 5, 7, 9, 11} mod 12residue class19.5 %
A191413a(n) = 3*n^2 - 2*n + 7polynomial100.0 %
A192607Nonludic numbers: complement of A003309sieve10.4 %
A193448a(n) = 4*(5*n^2 - 5*n + 1)polynomial100.0 %
A194431a(n) = 8*n^2 - 6*n - 1polynomial100.0 %
A194454a(n) = 12*n^2 + 2*n + 1polynomial100.0 %
A195018a(n) = n*(10*n-3)polynomial100.0 %
A195021a(n) = n*(14*n - 11)polynomial100.0 %
A195023a(n) = 14*n^2 - 4*npolynomial100.0 %
A195024a(n) = n*(14*n - 1)polynomial100.0 %
A195025a(n) = n*(14*n + 3)polynomial100.0 %
A195026a(n) = 7*n*(2*n + 1)polynomial100.0 %
A195027a(n) = 2*n*(7*n + 5)polynomial100.0 %
A195028a(n) = n*(14*n + 13)polynomial100.0 %
A195029a(n) = n*(14*n + 13) + 3polynomial100.0 %
A195086Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 2multiplicative18.7 %
A195087Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 3multiplicative19.4 %
A195088Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 4multiplicative19.9 %
A195089Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 5multiplicative20.5 %
A195090Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 6multiplicative20.7 %
A195091Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 7multiplicative21.2 %
A195092Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 8multiplicative21.8 %
A195093Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 9multiplicative22.8 %
A195131Numbers k such that 666k-1 is primeprime values19.6 %
A1952703-gap primes: Prime p is a term iff there is no prime between 3*p and 3*q, where q is the next prime after pprimes34.5 %
A195321a(n) = 18*n^2polynomial100.0 %
A195322a(n) = 20*n^2polynomial100.0 %
A195323a(n) = 22*n^2polynomial100.0 %
A195819Multiples of 29residue class9.7 %
A195824a(n) = 24*n^2polynomial100.0 %
A195905Primes of the form 10 * k^2 + 7primes100.0 %
A195943Zeroless prime powers: Intersection of A000961 and A052382powers23.6 %
A195993Numbers n such that 90n + 73 is primeprime values17.2 %
A196000Numbers k such that 90*k + 19 is primeprime values16.7 %
A196007Numbers n such that 90n + 83 is primeprime values16.8 %
A196507a(n) = n*(3*n^2 + 6*n + 1)polynomial100.0 %
A198017a(n) = n*(7*n + 11)/2 + 1polynomial100.0 %
A198273Primes not of the form p*q + p + q for any primes p and qprimes25.7 %
A198382Numbers n such that 90n + 37 is primeprime values16.9 %
A198772Numbers having exactly one representation by the quadratic form x^2 + xy + y^2 with 0 <= x <= yquadratic form27.1 %
A198773Numbers having exactly two representations by the quadratic form x^2+xy+y^2 with 0<=x<=yquadratic form30.4 %
A199325Primes having only {0, 1, 5} as digitsprimes39.7 %
A199326Primes having only {0, 1, 6} as digitsprimes40.2 %
A199327Primes having only {0, 1, 7} as digitsprimes33.1 %
A199329Primes having only {0, 1, 9} as digitsprimes33.2 %
A199340Primes having only {0, 3, 4} as digitsprimes38.2 %
A199341Primes having only {1, 3, 4} as digitsprimes30.8 %
A199342Primes having only {2, 3, 4} as digitsprimes36.9 %
A199345Primes having only {3, 4, 5} as digitsprimes36.7 %
A199346Primes having only {3, 4, 6} as digitsprimes38.2 %
A199347Primes having only {3, 4, 7} as digitsprimes33.8 %
A199348Primes having only {3, 4, 8} as digitsprimes39.6 %
A199349Primes having only {3, 4, 9} as digitsprimes32.4 %
A200995Numbers not expressible as a product of Lucas numberscomplement9.4 %
A201279a(n) = 6*n^2 + 10*n + 5polynomial100.0 %
A201313Primes of the form n^2 - 10primes100.0 %
A201314Primes of the form n^2 - 17primes100.0 %
A201473Primes of the form 2*k^2 + 3primes100.0 %
A201474Primes of the form 2n^2 + 5primes100.0 %
A201475Primes of the form 2n^2 + 7primes100.0 %
A201476Primes of the form 2*k^2 + 9primes100.0 %
A201477Primes of the form 3n^2 + 4primes100.0 %
A201478Primes of the form 3n^2 + 5primes100.0 %
A201479Primes of the form 3n^2 + 7primes100.0 %
A201480Primes of the form 3n^2 + 10primes100.0 %
A201482Primes of the form 5n^2 + 3primes100.0 %
A201484Primes of the form 5n^2 + 6primes100.0 %
A201486Primes of the form 5n^2 + 8primes100.0 %
A201487Primes of the form 5n^2 + 9primes100.0 %
A201600Primes of the form 6n^2 + 5primes100.0 %
A201601Primes of the form 6n^2 + 7primes100.0 %
A201602Primes of the form 7n^2 + 1primes100.0 %
A201605Primes of the form 7n^2 + 4primes100.0 %
A201607Primes of the form 7n^2 + 6primes100.0 %
A201609Primes of the form 7n^2 + 9primes100.0 %
A201610Primes of the form 7n^2 + 10primes100.0 %
A201611Primes of the form 8n^2 + 3primes100.0 %
A201612Primes of the form 8n^2 + 5primes100.0 %
A201705Primes of the form 8n^2 + 9primes100.0 %
A201706Primes of the form 9n^2 + 4primes100.0 %
A201707Primes of the form 9n^2 + 7primes100.0 %
A201708Primes of the form 9n^2 + 10primes100.0 %
A201709Primes of the form 10n^2 + 1primes100.0 %
A201710Primes of the form 10n^2 + 3primes100.0 %
A201711Primes of the form 10n^2 + 9primes100.0 %
A201712Primes of the form 2n^2 - 3primes100.0 %
A201713Primes of the form 2n^2 - 5primes100.0 %
A201714Primes of the form 2n^2 - 7primes100.0 %
A201715Primes of the form 3*m^2 - 2primes100.0 %
A201716Primes of the form 3*m^2 - 4primes100.0 %
A201717Primes of the form 3*m^2 - 5primes100.0 %
A201718Primes of the form 3*m^2 - 7primes100.0 %
A201734Numbers n such that 90*n + 47 is primeprime values16.8 %
A201739Numbers n such that 90*n + 29 is primeprime values18.2 %
A201781Primes of the form 3*m^2 - 8primes100.0 %
A201782Primes of the form 3n^2 - 10primes100.0 %
A201783Primes of the form 5n^2 - 1primes100.0 %
A201784Primes of the form 5n^2 - 2primes100.0 %
A201785Primes of the form 5n^2 - 3primes100.0 %
A201786Primes of the form 5*k^2 - 4primes100.0 %
A201787Primes of the form 5n^2 - 6primes100.0 %
A201788Primes of the form 5n^2 - 7primes100.0 %
A201789Primes of the form 5n^2 - 8primes100.0 %
A201790Primes of the form 5n^2 - 9primes100.0 %
A201791Primes of the form 6*k^2 - 5primes100.0 %
A201792Primes of the form 6n^2 - 7primes100.0 %
A201793Primes of the form 7n^2 - 1primes100.0 %
A201804Numbers k such that 90*k + 11 is primeprime values17.2 %
A201816Numbers k such that 90*k + 13 is primeprime values16.6 %
A201817Numbers k such that 90*k + 67 is primeprime values17.6 %
A201818Numbers k such that 90*k + 49 is primeprime values16.6 %
A201819Numbers n such that 90*n + 31 is primeprime values17.7 %
A201820Numbers k such that 90*k + 23 is primeprime values17.3 %
A201822Numbers k such that 90*k + 77 is primeprime values16.2 %
A201848Primes of the form 7n^2 - 2primes100.0 %
A201849Primes of the form 7n^2 - 3primes100.0 %
A201850Primes of the form 7n^2 - 4primes100.0 %
A201851Primes of the form 7n^2 - 5primes100.0 %
A201852Primes of the form 7n^2 - 6primes100.0 %
A201853Primes of the form 7n^2 - 8primes100.0 %
A201854Primes of the form 7n^2 - 9primes100.0 %
A201856Primes of the form 8n^2 - 3primes100.0 %
A201857Primes of the form 8n^2 - 5primes100.0 %
A201858Primes of the form 8n^2 - 7primes100.0 %
A201859Primes of the form 8n^2 - 9primes100.0 %
A201860Primes of the form 9n^2 - 2primes100.0 %
A201960Primes of the form 9n^2 - 5primes100.0 %
A201961Primes of the form 9n^2 - 8primes100.0 %
A201962Primes of the form 10n^2 - 3primes100.0 %
A201964Primes of the form 10n^2 - 9primes100.0 %
A202083Primes of the form 16n^2 + 121primes100.0 %
A202101Numbers k such that 90*k + 59 is primeprime values16.7 %
A202104Numbers k such that 90*k + 41 is primeprime values17.2 %
A202105Numbers k such that 90*k + 43 is primeprime values17.9 %
A202110Numbers k such that 90*k + 7 is primeprime values16.5 %
A202112Numbers k such that 90*k + 79 is primeprime values17.5 %
A202113Numbers k such that 90*k + 61 is primeprime values16.5 %
A202114Numbers k such that 90*k + 53 is primeprime values17.7 %
A202115Numbers k such that 90*k + 17 is primeprime values17.3 %
A202116Numbers k such that 90*k + 89 is primeprime values16.7 %
A202129Numbers n such that 90n + 71 is primeprime values17.5 %
A202267Numbers in which all digits are noncomposites (1, 2, 3, 5, 7) or 0digit rule15.7 %
A202268Numbers in which all digits are neither primes nor zero, i.e., are members of (1, 4, 6, 8, 9)digit rule15.8 %
A202803a(n) = n*(5*n+1)polynomial100.0 %
A202804a(n) = n*(6*n+4)polynomial100.0 %
A202822Numbers of the form 3*(x^2 + xy + y^2 + x + y) + 1 where x and y are integersquadratic form28.4 %
A203463Where Golay-Rudin-Shapiro sequence A020985 is positivebinary rule11.1 %
A203551a(n) = n*(5n^2 + 3n + 4) / 6polynomial100.0 %
A203552a(n) = n*(5*n^2 - 3*n + 4) / 6polynomial100.0 %
A204542Numbers that are congruent to {1, 4, 11, 14} mod 15residue class16.7 %
A204666Primes p such that q-p = 54, where q is the next prime after pprimes59.3 %
A204674a(n) = 4*n^3 + 5*n^2 + 2*n + 1polynomial100.0 %
A204675a(n) = 16*n^2 + 2*n + 1polynomial100.0 %
A208177Primes of the form 128*k + 1primes52.8 %
A208178Primes of the form 256*k + 1primes58.1 %
A208270Primes containing a digit 1primes24.8 %
A208272Primes containing a digit 2primes24.3 %
A209061Exponentially squarefree numbersmultiplicative9.7 %
A209294a(n) = (7*n^2 - 7*n + 4)/2polynomial100.0 %
A210440a(n) = 2*n*(n+1)*(n+2)/3polynomial100.0 %
A210479Primes p with p-1 and p+1 both practical: "Sandwich of the first kind"primes54.5 %
A210527a(n) = 9*n^2 + 39*n + 83polynomial100.0 %
A212160Numbers that are congruent to {2, 10} mod 13residue class23.5 %
A212164Numbers k such that the maximum exponent in its prime factorization is greater than the number of positive exponents (A051903(k) > A001221(k))multiplicative13.9 %
A212165Numbers k such that the maximum exponent in its prime factorization is not less than the number of positive exponents (A051903(k) >= A001221(k))multiplicative14.8 %
A212166Numbers k such that the maximum exponent in its prime factorization equals the number of positive exponents (A051903(k) = A001221(k))multiplicative18.1 %
A212168Numbers n such that the maximal exponent in its prime factorization is less than the number of positive exponents (A051903(n) < A001221(n))multiplicative11.9 %
A212331a(n) = 5*n*(n+5)/2polynomial100.0 %
A212374Primes congruent to 1 mod 23primes46.2 %
A212492Prime p such that p, p+10, p+12 are all primesprimes59.0 %
A212525Primes containing a digit 3primes26.2 %
A212656a(n) = 5*n^2 + 1polynomial100.0 %
A212707Semiprimes of the form 5*n^2 + 1multiplicative100.0 %
A213382Numbers n such that n^n mod (n + 2) = npowers41.4 %
A214423Numbers k palindromic in only one base b, 2 <= b <= 10digit rule42.4 %
A214584Integers whose decimal representation has only digits in {4,5,7}digit rule11.0 %
A214588Primes p such that p mod 16 < 8primes28.3 %
A214659a(n) = n*(7*n^2 - 3*n - 1)/3polynomial100.0 %
A214660a(n) = 9*n^2 - 11*n + 3polynomial100.0 %
A214675a(n) = 9*n^2 - 13*n + 5polynomial100.0 %
A214703Primes having only {2, 3, 5} as digitsprimes38.3 %
A214704Primes that contain only the digits (2, 3, 7)primes34.6 %
A214705Primes that contain only the digits (2, 5, 7)primes41.0 %
A214732a(n) = 25*n^2 + 15*n + 1021polynomial100.0 %
A214888Primes congruent to {2, 3} mod 11primes37.3 %
A214889Primes congruent to {2, 3} mod 13primes38.1 %
A214890Primes congruent to {2, 3} mod 17primes39.9 %
A215101Primes congruent to {2, 3} mod 19primes40.3 %
A215102Primes congruent to {2, 3, 5} mod 11primes34.0 %
A215103Primes congruent to {2, 3, 5} mod 13primes35.0 %
A215104Primes congruent to {2, 3, 5} mod 17primes36.5 %
A215105Primes congruent to {2, 3, 5} mod 19primes37.4 %
A215106Primes congruent to {3, 5, 6} mod 11primes31.8 %
A215131Primes congruent to {3, 5, 6} mod 13primes32.4 %
A215132Primes congruent to {3, 5, 6} mod 17primes34.2 %
A215133Primes congruent to {3, 5, 6} mod 19primes34.8 %
A215134Primes congruent to {1, 2, 3} mod 11primes32.5 %
A215135Primes congruent to {1, 2, 3} mod 13primes33.3 %
A215153Primes congruent to {1, 2, 3} mod 17primes34.6 %
A215154Primes congruent to {1, 2, 3} mod 19primes34.8 %
A215155Primes congruent to {2, 3, 5, 7} mod 13primes32.9 %
A215156Primes congruent to {2, 3, 5, 7} mod 17primes34.5 %
A215157Primes congruent to {2, 3, 5, 7} mod 19primes35.1 %
A215161Primes congruent to {2, 3, 5, 7, 11} mod 17primes31.9 %
A215162Primes congruent to {2, 3, 5, 7, 11} mod 19primes32.8 %
A215163Primes congruent to {1, 4} mod 11primes37.0 %
A215164Primes congruent to {1, 4} mod 13primes38.4 %
A215165Primes congruent to {1, 4} mod 17primes39.4 %
A215166Primes congruent to {1, 4} mod 19primes40.7 %
A215167Primes congruent to {2, 5} mod 11primes37.2 %
A215168Primes congruent to {2, 5} mod 13primes38.6 %
A215169Primes congruent to {2, 5} mod 17primes39.3 %
A215170Primes congruent to {2, 5} mod 19primes40.8 %
A215206Primes congruent to {2, 7} mod 11primes37.0 %
A215207Primes congruent to {2, 7} mod 13primes38.0 %
A215208Primes congruent to {2, 7} mod 17primes40.0 %
A215209Primes congruent to {2, 7} mod 19primes40.4 %
A215210Primes congruent to {2, 5, 7} mod 11primes33.7 %
A215211Primes congruent to {2, 5, 7} mod 13primes35.0 %
A215212Primes congruent to {2, 5, 7} mod 17primes36.7 %
A215213Primes congruent to {2, 5, 7} mod 19primes37.6 %
A215214Primes congruent to {0, 1, 2, 5} mod 11primes32.7 %
A215215Primes congruent to {0, 1, 2, 5} mod 13primes33.7 %
A215273Primes congruent to {0, 1, 2, 5} mod 17primes34.8 %
A215274Primes congruent to {0, 1, 2, 5} mod 19primes35.2 %
A215275Primes congruent to {2, 4, 5, 6} mod 11primes30.9 %
A215276Primes congruent to {2, 4, 5, 6} mod 13primes32.2 %
A215277Primes congruent to {2, 4, 5, 6} mod 17primes33.2 %
A215278Primes congruent to {2, 4, 5, 6} mod 19primes33.8 %
A215279Primes congruent to {2, 3, 4} mod 11primes32.5 %
A215280Primes congruent to {2, 3, 4} mod 13primes32.7 %
A215281Primes congruent to {2, 3, 4} mod 17primes35.1 %
A215282Primes congruent to {2, 3, 4} mod 19primes34.1 %
A215302Primes congruent to {1, 2, 3, 4} mod 11primes30.2 %
A215303Primes congruent to {1, 2, 3, 4} mod 13primes30.9 %
A215304Primes congruent to {1, 2, 3, 4} mod 17primes32.1 %
A215305Primes congruent to {1, 2, 3, 4} mod 19primes32.4 %
A215306Primes congruent to {1, 2, 3, 5} mod 11primes31.2 %
A215307Primes congruent to {1, 2, 3, 5} mod 13primes32.1 %
A215308Primes congruent to {1, 2, 3, 5} mod 17primes33.2 %
A215309Primes congruent to {1, 2, 3, 5} mod 19primes33.9 %
A215310Primes congruent to {1, 2, 3, 4, 5} mod 11primes29.3 %
A215311Primes congruent to {1, 2, 3, 4, 5} mod 13primes30.4 %
A215312Primes congruent to {1, 2, 3, 4, 5} mod 17primes31.2 %
A215313Primes congruent to {1, 2, 3, 4, 5} mod 19primes31.9 %
A215314Primes congruent to {2, 3, 4, 5} mod 11primes31.2 %
A215315Primes congruent to {2, 3, 4, 5} mod 13primes31.9 %
A215316Primes congruent to {2, 3, 4, 5} mod 17primes33.3 %
A215317Primes congruent to {2, 3, 4, 5} mod 19primes33.6 %
A215318Primes congruent to {1, 2, 3, 5, 6} mod 11primes27.4 %
A215319Primes congruent to {1, 2, 3, 5, 6} mod 13primes30.1 %
A215320Primes congruent to {1, 2, 3, 5, 6} mod 17primes31.2 %
A215321Primes congruent to {1, 2, 3, 5, 6} mod 19primes31.8 %
A215322Primes congruent to {1, 2, 3, 4, 6} mod 11primes26.3 %
A215323Primes congruent to {1, 2, 3, 4, 6} mod 13primes29.4 %
A215324Primes congruent to {1, 2, 3, 4, 6} mod 17primes30.3 %
A215325Primes congruent to {1, 2, 3, 4, 6} mod 19primes30.8 %
A215350Primes congruent to {2, 3, 4, 6} mod 11primes29.6 %
A215351Primes congruent to {2, 3, 4, 6} mod 13primes30.6 %
A215352Primes congruent to {2, 3, 4, 6} mod 17primes32.1 %
A215646a(n) = n * (11*n^2 + 6*n + 1) / 6polynomial100.0 %
A215927Primes having at least one digit that is not primeprimes23.1 %
A216838Odd primes for which 2 is not a primitive rootprimes26.8 %
A216968Numbers k such that 2*k^2 + 3 is primeprime values25.6 %
A216970Primes congruent to 1 mod 37primes49.3 %
A217039Primes having only {4, 5, 7} as digitsprimes37.4 %
A217139Numbers n such that phi(n) = phi(n+12), with Euler's totient function phi = A000010divisor functions38.2 %
A217495Primes of the form 2*n^2 + 46*n + 21primes100.0 %
A217496Primes of the form 2*n^2 + 50*n + 23primes100.0 %
A217498Primes of the form 2*n^2 + 58*n + 27primes100.0 %
A217500Primes of the form 2*n^2 + 74*n + 35primes100.0 %
A217501Primes of the form 2*n^2 + 78*n + 37primes100.0 %
A217620Primes of the form 2*n^2 + 82*n + 39primes100.0 %
A217775a(n) = n*(n+1) + (n+2)*(n+3) + (n+4)*(n+5)polynomial100.0 %
A217776a(n) = n*(n+1) + (n+2)*(n+3) + (n+4)*(n+5) + (n+6)*(n+7)polynomial100.0 %
A217873a(n) = 4*n*(n^2 + 2)/3polynomial100.0 %
A218152a(n) = 1 + n + ((n-1)*n^2)/2polynomial100.0 %
A218155Numbers congruent to 2, 3, 6, 11 mod 12residue class14.5 %
A218471a(n) = n*(7*n-3)/2polynomial100.0 %
A219054a(n) = (8*n^3 + 3*n^2 + n) / 6polynomial100.0 %
A220081Primes of the form 15*k^2 - 15*k + 17primes100.0 %
A220083a(n) = (15*n^2 + 9*n + 2)/2polynomial100.0 %
A220084a(n) = (n + 1)*(20*n^2 + 19*n + 6)/6polynomial100.0 %
A222465a(n) = 4*n^2 + 3polynomial100.0 %
A224467Numbers n such that 27*n+1 is primeprime values18.7 %
A224870Numbers m such that m^2 + (m+3)^2 is primeprime values22.1 %
A224889Numbers n such that 90n + 91 is primeprime values16.3 %
A225423Primes p such that p + 70000000 is also primeprimes44.4 %
A225550Primes p such that p^2 mod 37 is primeprimes35.5 %
A225856Primes p such that p^2 + 1 is squarefreeprimes24.2 %
A226449a(n) = n*(5*n^2-8*n+5)/2polynomial100.0 %
A226450a(n) = n*(3*n^2 - 5*n + 3)polynomial100.0 %
A226451a(n) = n*(7*n^2-12*n+7)/2polynomial100.0 %
A226488a(n) = n*(13*n - 9)/2polynomial100.0 %
A226489a(n) = n*(15*n-11)/2polynomial100.0 %
A226490a(n) = n*(19*n-15)/2polynomial100.0 %
A226491a(n) = n*(21*n-17)/2polynomial100.0 %
A226492a(n) = n*(11*n-5)/2polynomial100.0 %
A227144Numbers that are congruent to {1, 2, 7, 17, 23} modulo 24residue class14.9 %
A227146Numbers that are congruent to {5, 11, 13, 14, 19} modulo 24residue class14.9 %
A227776a(n) = 6*n^2 + 1polynomial100.0 %
A227793Numbers whose digital sum is a multiple of 5digit rule20.3 %
A227916Primes that remain prime when the leftmost digit is removedprimes38.5 %
A228121Numbers n such that 3n - 4 is primeprime values26.7 %
A228137Numbers that are congruent to {1, 4} mod 12residue class30.2 %
A228141Numbers that are congruent to {1, 5} mod 20residue class31.8 %
A228184Numbers k such that k^2 + k + 41 is semiprimemultiplicative13.1 %
A228227Primes congruent to {7, 11} mod 16primes33.3 %
A228228Primes congruent to {3, 5, 13, 15} mod 16primes28.2 %
A229183a(n) = n*(n^2 + 3)/2polynomial100.0 %
A229854Primes of the form 384*k + 1primes64.3 %
A229856Primes of the form 384*k + 257primes64.0 %
A229947Primes congruent to {1, 11, 13, 17, 19, 29} mod 30primes25.3 %
A230018a(n) = (9*n^3 + 5*n)/2polynomial100.0 %
A230091Numbers of the form k + wt(k) for exactly two distinct k, where wt(k) = A000120(k) is the binary weight of kbinary rule17.6 %
A230092Numbers of the form k + wt(k) for exactly three distinct k, where wt(k) = A000120(k) is the binary weight of kbinary rule30.4 %
A230223Primes p such that 3*p-4, 3*p-10, and 3*p-14 are all primeprimes65.5 %
A230391Numbers m such that 232*m^2+1 is primeprime values17.6 %
A230577Positive integers that have exactly 6 odd divisorsdivisor functions24.9 %
A230633Numbers n such that m + (sum of digits in base-4 representation of m) = n has exactly one solutiondigit rule11.7 %
A230634Numbers n such that m + (sum of digits in base-4 representation of m) = n has exactly two solutionsdigit rule18.1 %
A230853Numbers n such that m + (sum of digits in base-3 representation of m) = n has exactly one solutiondigit rule20.3 %
A230854Numbers n such that m + (sum of digits in base-3 representation of m) = n has exactly two solutionsdigit rule11.3 %
A231607Primes p such that p + 600 is also primeprimes33.8 %
A232495a(n) = 9*n^3/2 - 21*n^2/2 + 8*n - 4polynomial100.0 %
A233010In balanced ternary notation, either a palindrome or becomes a palindrome if trailing 0's are omitteddigit rule68.9 %
A234095Primes p such that 2*p + 1 is semiprimeprimes34.8 %
A234695Primes p with prime(p) - p + 1 also primeprimes38.7 %
A235592Numbers k such that k*(k+1) - prime(k) is primeprimes21.9 %
A236119Primes p with prime(p) - p - 1 and prime(p) - p + 1 both primeprimes57.0 %
A236267a(n) = 8*n^2 + 3*n + 1polynomial100.0 %
A236464Primes p with prime(p) + 2 and prime(p) + 6 both primeprimes60.6 %
A236562Numbers n such that A049820(x) = n has a solutiondivisor functions11.9 %
A237616a(n) = n*(n + 1)*(5*n - 4)/2polynomial100.0 %
A237617a(n) = n*(n + 1)*(17*n - 14)/6polynomial100.0 %
A237618a(n) = n*(n + 1)*(19*n - 16)/6polynomial100.0 %
A237991a(n) = 991*n^2 + 1polynomial100.0 %
A238242Primes p such that p^2+p+41 is also primeprimes34.2 %
A239325a(n) = 6*n^2 + 8*n + 1polynomial100.0 %
A239449a(n) = 7*n^2 - 5*n + 1polynomial100.0 %
A241748a(n) = n^2 + 12polynomial100.0 %
A241749a(n) = n^2 + 13polynomial100.0 %
A241750a(n) = n^2 + 15polynomial100.0 %
A241751a(n) = n^2 + 16polynomial100.0 %
A241847a(n) = n^2 + 17polynomial100.0 %
A241848a(n) = n^2 + 18polynomial100.0 %
A241849a(n) = n^2 + 19polynomial100.0 %
A241850a(n) = n^2 + 20polynomial100.0 %
A241851a(n) = n^2 + 21polynomial100.0 %
A241889a(n) = n^2 + 23polynomial100.0 %
A241890a(n) = n^2 + 24polynomial100.0 %
A242260Primes p such that p^2-2 is semiprimeprimes31.9 %
A242330Numbers k such that k^2 + 2 is a semiprimemultiplicative22.1 %
A242331Numbers k such that k^2 + 3 is a semiprimemultiplicative14.7 %
A242332Numbers k such that k^2 + 4 is a semiprimemultiplicative25.2 %
A242333Numbers k such that k^2 + 5 is a semiprimemultiplicative17.0 %
A242412a(n) = (2*n-1)^2 + 14polynomial100.0 %
A242476Primes p such that p + 22 is also primeprimes46.7 %
A242659a(n) = n*(n^2 - 3*n + 4)polynomial100.0 %
A242708Primes p such that p^2 + p + 41 is semiprimeprimes29.1 %
A243138a(n) = n^2 + 15*n + 13polynomial100.0 %
A243173Numbers of the form x^2+15y^2quadratic form30.3 %
A243367Primes p such that p^2 + 10 is primeprimes43.1 %
A243436Numbers n such that n^2-n-1 is semiprimemultiplicative14.2 %
A243450Primes of the form n^2 + 15primes100.0 %
A243451Primes of the form n^2 + 16primes100.0 %
A243520Numbers that are congruent to {0, 8} mod 11residue class21.8 %
A243544Primes p such that p^2 - p + 1 is semiprimeprimes36.5 %
A243595Primes p such that 3 + 2*p^2 is also primeprimes48.7 %
A243762a(n) = 4*n^3 + 5polynomial100.0 %
A243937Even numbers n>=6 for which lpf(n-1) > lpf(n-3), where lpf = least prime factormultiplicative15.1 %
A244037Numbers of the form x^2+14y^2quadratic form17.7 %
A244082a(n) = 32*n^2polynomial100.0 %
A244630a(n) = 17*n^2polynomial100.0 %
A244631a(n) = 19*n^2polynomial100.0 %
A244632a(n) = 23*n^2polynomial100.0 %
A244633a(n) = 26*n^2polynomial100.0 %
A244634a(n) = 27*n^2polynomial100.0 %
A244635a(n) = 29*n^2polynomial100.0 %
A244636a(n) = 30*n^2polynomial100.0 %
A244725a(n) = 5*n^3polynomial100.0 %
A244726a(n) = 6*n^3polynomial100.0 %
A244727a(n) = 7*n^3polynomial100.0 %
A244728a(n) = 9*n^3polynomial100.0 %
A245048Primes p such that p^2 + 28 is primeprimes37.3 %
A245301a(n) = n*(7*n^2 + 15*n + 8)/6polynomial100.0 %
A245590Primes p such that p^2 + 6 is a semiprimeprimes36.8 %
A246172a(n) = (n^2 + 9*n - 8)/2polynomial100.0 %
A246281Numbers k for which A003961(k) < 2*k; Numbers n such that if n = product_{k >= 1} (p_k)^(c_k), then product_{k >= 1} (p_{k+1})^(c_k) < 2*n, where p_k indicates the k-th prime, A000040(k)multiplicative9.2 %
A246282Numbers k for which A003961(k) > 2*k; numbers n such that if n = Product_{k >= 1} (p_k)^(c_k), then Product_{k >= 1} (p_{k+1})^(c_k) > 2*n, where p_k indicates the k-th prime, A000040(k)multiplicative14.2 %
A246965Numbers n such that 19*n-(n+19) is a primeprime values18.0 %
A247052Primes composed of only digits with line segments or both line segments and curves {1, 2, 4, 5, 7}primes32.5 %
A247155a(n) = 31*n^2 + 1polynomial100.0 %
A247541a(n) = 7*n^2 + 1polynomial100.0 %
A247676Odd composite numbers congruent to 2 modulo 9residue class39.5 %
A247678Odd composite numbers congruent to 4 modulo 9residue class39.3 %
A247681Odd nonprimes congruent to 1 modulo 9residue class39.4 %
A247792a(n) = 9*n^2 + 1polynomial100.0 %
A247881Numbers of the form x^2 + 13*y^2quadratic form20.9 %
A248221Numbers m such that 52*m + 1 is primeprime values23.4 %
A248368Primes p such that 52*p + 1 is primeprimes47.8 %
A249354a(n) = n*(3*n^2 + 3*n + 1)polynomial100.0 %
A249374Prime numbers Q such that the concatenation Q,1,Q is primeprimes48.3 %
A249606Primes of the form 2k^2 + k + 2primes100.0 %
A250036Numbers n such that m = floor(n/4) is coprime to n and, if nonzero, m is also a term of the sequenceself-referential11.8 %
A250046Numbers n such that m = floor(n/7) is coprime to n and, if nonzero, m is also a term of the sequenceself-referential9.2 %
A250047Numbers n such that m = floor(n/7) is not coprime to n and, if nonzero, m is also a term of the sequenceself-referential11.2 %
A250048Numbers n such that m = floor(n/6) is coprime to n and, if nonzero, m is also a term of the sequenceself-referential8.6 %
A250049Numbers n such that m = floor(n/6) is not coprime to n and, if nonzero, m is also a term of the sequenceself-referential14.8 %
A251726Numbers n > 1 for which gpf(n) < lpf(n)^2, where lpf and gpf (least and greatest prime factor of n) are given by A020639(n) and A006530(n)smooth18.1 %
A251728Semiprimes p*q for which p <= q < p^2multiplicative26.4 %
A252089Primes p such that p + 26 is primeprimes46.9 %
A252090Primes p such that p + 28 is also primeprimes45.9 %
A252091Primes p such that p + 34 is primeprimes46.4 %
A252994Multiples of 26residue class9.6 %
A253239Numbers k such that k^2 + k + 72491 is primeprime values15.0 %
A254407a(n) = n*(n+1)*(11*n +10)/6polynomial100.0 %
A254963a(n) = n*(11*n + 3)/2polynomial100.0 %
A255211a(n) = n*(n+1)*(7*n+2)/6polynomial100.0 %
A255634Numbers n such that 1 + 16n^2 is primeprime values24.3 %
A255687a(n) = n*(n + 1)*(7*n + 11)/6polynomial100.0 %
A255842a(n) = 2*n^2 + 12polynomial100.0 %
A255843a(n) = 2*n^2 + 4polynomial100.0 %
A255844a(n) = 2*n^2 + 6polynomial100.0 %
A255845a(n) = 2*n^2 + 10polynomial100.0 %
A255846a(n) = 2*n^2 + 14polynomial100.0 %
A255847a(n) = 2*n^2 + 16polynomial100.0 %
A255848a(n) = 2*n^2 + 18polynomial100.0 %
A256177Primes congruent to {8, 13, 18, 23} mod 25primes38.9 %
A256290Numbers which have only digits 4 and 5 in base 10digit rule12.4 %
A256291Numbers which have only digits 5 and 6 in base 10digit rule10.7 %
A256292Numbers which have only digits 6 and 7 in base 10digit rule8.6 %
A256340Numbers which have only digits 7 and 8 in base 10digit rule10.0 %
A256374Primes of the form 7*k^2 + 7*k + 17primes100.0 %
A256376Primes of the form 10n^2 - 90n + 163primes100.0 %
A256585Primes of the form 3n^2 + 39n + 37primes100.0 %
A256601Numbers n such that the decimal expansions of both n and n^2 have 1 as smallest digit and 9 as largest digitdigit rule20.2 %
A256634Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 7 as largest digitdigit rule22.2 %
A256674Numbers n such that n^2 + n + 712329866165608771 is primeprime values25.2 %
A256716a(n) = n*(n+1)*(22*n-19)/6polynomial100.0 %
A256718a(n) = n*(n+1)*(7*n-6)/2polynomial100.0 %
A256775Primes of the form n^2 + 81primes100.0 %
A256776Primes of form n^2 + 256primes100.0 %
A256777Primes of form n^2 + 625primes100.0 %
A256833a(n) = (4*n+3)*(4*n+2)polynomial100.0 %
A256834Primes of form n^2 + 1296primes100.0 %
A256835Primes of form n^2 + 2401primes100.0 %
A256836Primes of form n^2 + 4096primes100.0 %
A256837Primes of form n^2 + 6561primes100.0 %
A256838Primes of form n^2 + 10000primes100.0 %
A256839Primes of form n^2 + 14641primes100.0 %
A256840Primes of form n^2 + 20736primes100.0 %
A256841Primes of form n^2 + 28561primes100.0 %
A256857a(n) = n*(n^2 + 3*n - 2)/2polynomial100.0 %
A257042a(n) = (3*n+7)*n^2polynomial100.0 %
A257093a(n) = n*(n+1)*(13*n+2)/6polynomial100.0 %
A257163Primes of the form 3n^2 + 2primes100.0 %
A257210Numbers n such that the decimal expansions of both n and n^2 have 1 as smallest digit and 7 as largest digitdigit rule34.4 %
A257211Numbers n such that the decimal expansions of both n and n^2 have 1 as smallest digit and 8 as largest digitdigit rule24.2 %
A257219Numbers that have at least one divisor containing the digit 2 in base 10divisor functions10.6 %
A257220Numbers that have at least one divisor containing the digit 3 in base 10divisor functions11.3 %
A257368Numbers n such that the decimal expansions of both n and n^2 have 2 as smallest digit and 8 as largest digitdigit rule31.2 %
A257667Primes containing a digit 5primes25.6 %
A257668Primes containing a digit 7primes27.3 %
A258261Primes p such that 3p - 4 is also primeprimes37.6 %
A258582a(n) = n*(2*n + 1)*(4*n + 1)/3polynomial100.0 %
A258617a(n) = (4*n+8)*n^2polynomial100.0 %
A258618a(n) = (4*n+9)*n^2polynomial100.0 %
A258663Numbers n such that 9n-1 is primeprime values18.8 %
A258721a(n) = 24*n^2 + 52*n + 29polynomial100.0 %
A258992Primes p such that p^2 - 8 is also primeprimes40.1 %
A259055a(n) = 9*n^2 + 18*n + 7polynomial100.0 %
A259555a(n) = 2*n^2 - 2*n + 17polynomial100.0 %
A259614Numbers congruent to {17,29} mod 36residue class37.2 %
A259749Numbers that are congruent to {1,2,5,7,10,11,13,17,19,23} mod 24residue class6.6 %
A259750Numbers that are congruent to {14, 22} mod 24residue class18.0 %
A259751Numbers that are congruent to {8, 16} mod 24residue class0.0 %
A259754Numbers that are congruent to {3,9,15,18,21} mod 24residue class14.7 %
A259755Numbers that are congruent to {4, 20} mod 24residue class9.6 %
A260044Primes having only {0, 1, 3} as digitsprimes30.3 %
A260125Primes having only {0, 2, 3} as digitsprimes37.5 %
A260126Primes having only {2, 3, 6} as digitsprimes39.5 %
A260127Primes having only {2, 3, 8} as digitsprimes40.3 %
A260128Primes having only {2, 3, 9} as digitsprimes32.6 %
A260223Primes having only {3, 5, 0} as digitsprimes39.8 %
A260224Primes having only {1, 3, 5} as digitsprimes32.5 %
A260225Primes having only {3, 5, 6} as digitsprimes37.8 %
A260226Primes having only {3, 5, 8} as digitsprimes40.5 %
A260227Primes having only {3, 5, 9} as digitsprimes33.2 %
A260260a(n) = n*(16*n^2 - 21*n + 7)/2polynomial100.0 %
A260266Primes having only {0, 1, 4} as digitsprimes39.5 %
A260267Primes having only {1, 2, 4} as digitsprimes39.0 %
A260682Löschian numbers (A003136) of the form 6*k+1quadratic form32.2 %
A261034Numbers m such that 3*m is squarefreemultiplicative5.3 %
A261521a(n) = n^2 + 2*n + 29polynomial100.0 %
A261893a(n) = (n+1)^3 - n^2polynomial100.0 %
A262000a(n) = n^2*(7*n - 5)/2polynomial100.0 %
A262221a(n) = 25*n*(n + 1)/2 + 1polynomial100.0 %
A263226a(n) = 15*n^2 - 13*npolynomial100.0 %
A263228a(n) = 2*n*(16*n - 13)polynomial100.0 %
A264443a(n) = n*(n + 5)*(n + 10)/6polynomial100.0 %
A264444a(n) = n*(n + 7)*(n + 14)/6polynomial100.0 %
A264445a(n) = n*(n + 11)*(n + 22)/6polynomial100.0 %
A264790Numbers k such that k^2 + 17 is primeprime values22.9 %
A267290Primes of the form 11*k^2-11*k+7primes100.0 %
A267522a(n) = 4*(n + 1)*(n + 2)*(4*n + 3)/3polynomial100.0 %
A267984Numbers congruent to {17, 23} mod 30residue class36.8 %
A267985Numbers congruent to {7, 13} mod 30residue class36.7 %
A268201a(n) = 4*n^3 - 6*n^2 + 3*n - 1polynomial100.0 %
A268351a(n) = 3*n*(9*n - 1)/2polynomial100.0 %
A268484a(n) = (n + 1)*(4*n^2 + 14*n + 9)/3polynomial100.0 %
A268577Numbers m such that 3*m^2-5 is a primeprime values21.7 %
A268581a(n) = 2*n^2 + 8*n + 5polynomial100.0 %
A268620Numbers whose digital sum is a multiple of 4digit rule20.2 %
A268684a(n) = n*(n + 1)*(4*n - 1)/3polynomial100.0 %
A269232a(n) = (n + 1)*(6*n^2 + 15*n + 4)/2polynomial100.0 %
A269342a(n) = (n + 1)*(2*n + 1)*(4*n + 9)/3polynomial100.0 %
A269457a(n) = 5*(n + 1)*(n + 4)/2polynomial100.0 %
A269819Numbers that are congruent to {5, 11, 13, 19} mod 24residue class21.3 %
A270109a(n) = n^3 + (n+1)*(n+2)polynomial100.0 %
A270189Numbers n for which (prime(n+1)-prime(n)) is not a multiple of threeprimes12.3 %
A270190Numbers n for which prime(n+1)-prime(n) is a multiple of threeprimes13.7 %
A270867a(n) = n^3 + 2*n^2 + 4*n + 1polynomial100.0 %
A271347Primes p such that p + 38 is also primeprimes46.9 %
A271366Primes of the form 272259344081 + 2*n^2primes95.1 %
A271508Numbers that are congruent to {1,4} mod 10residue class21.5 %
A271649a(n) = 2*(n^2 - n + 2)polynomial100.0 %
A271666Primes p such that 4*p^2+4*p-1 is primeprimes40.0 %
A271667Primes p such that 6*p^2+6*p-1 is primeprimes42.4 %
A271740a(n) = 3*n^2 - 2*n + 2polynomial100.0 %
A271779a(n) = n^3 + 2*n^2 + 5*n + 11polynomial100.0 %
A271818Primes of the form 33164857769 + 2*n^2primes98.4 %
A271819Primes of the form 159587584529 + 2*n^2primes97.0 %
A271820Primes of the form 236241327599 + 2*n^2primes96.6 %
A271828a(n) = 4*n^3 - 18*n^2 + 27*n - 12polynomial100.0 %
A271980Numbers k such that 3*k^2 + 39*k + 37 is primeprime values16.7 %
A271981Primes p such that p + 40 is also primeprimes44.5 %
A271982Primes p such that p + 42 is also primeprimes34.9 %
A272039a(n) = 10*n^2 + 4*n + 1polynomial100.0 %
A272159Numbers k such that abs(8*k^2 - 488*k + 7243) is primeprime values15.6 %
A272176Primes p such that p + 44 is also primeprimes46.2 %
A272284Numbers n such that 43*n^2 - 537*n + 2971 is primeprime values15.9 %
A272378a(n) = n*(6*n^2 - 8*n + 3)polynomial100.0 %
A272933Numbers of the form x^2 + 12*y^2quadratic form26.6 %
A272975Numbers that are congruent to {0,7} mod 12residue class30.2 %
A273159Numbers whose digit sum is divisible by 7digit rule23.2 %
A273188Numbers whose digit sum is divisible by 8digit rule24.8 %
A273220a(n) = 8n^2 - 12n + 1polynomial100.0 %
A273366a(n) = 10*n^2 + 10*n + 2polynomial100.0 %
A274077a(n) = n^3 + 4polynomial100.0 %
A274319Numbers whose digit sum is divisible by 6digit rule9.0 %
A274357Numbers n such that n and n+1 both have 8 divisorsdivisor functions24.7 %
A274546Numbers m such that 5*m is squarefreemultiplicative11.1 %
A275591a(n) = n^2 + 9*n + 1polynomial100.0 %
A275709a(n) = 2*n^3 + 3*n^2polynomial100.0 %
A275874a(n) = (n-4)*(n+1)*(n+3)/6polynomial100.0 %
A276037Numbers using only digits 1 and 5digit rule18.4 %
A276039Numbers using only digits 1 and 7digit rule17.2 %
A276137Numbers without the decimal digits 2, 4, 6 and 8digit rule15.5 %
A276138Numbers without the decimal digits 1, 3, 5 and 7digit rule12.9 %
A276378Numbers k such that 6*k is squarefreemultiplicative11.4 %
A276713Numbers n such that n and n+3 have the same number of divisors (A000005)multiplicative20.3 %
A276819a(n) = (9*n^2 - n)/2 + 1polynomial100.0 %
A277108a(n) = 4*n*(n+5)polynomial100.0 %
A277568Numbers k such that k/6^m == 2 (mod 6), where 6^m is the greatest power of 6 that divides kresidue class18.8 %
A277588Numbers k such that k/10^m == 1 mod 10, where 10^m is the greatest power of 10 that divides nresidue class30.2 %
A277589Numbers k such that k/10^m == 2 mod 10, where 10^m is the greatest power of 10 that divides nresidue class21.4 %
A277590Numbers k such that k/10^m == 3 mod 10, where 10^m is the greatest power of 10 that divides nresidue class30.4 %
A277591Numbers k such that k/10^m == 4 mod 10, where 10^m is the greatest power of 10 that divides nresidue class21.4 %
A277593Numbers k such that k/10^m == 6 mod 10, where 10^m is the greatest power of 10 that divides nresidue class21.6 %
A277976a(n) = n*(3*n + 23)polynomial100.0 %
A277978a(n) = 3*n*(n+3)polynomial100.0 %
A277979a(n) = 4*n^2 + 18*npolynomial100.0 %
A277980a(n) = 12*n^2 + 18*npolynomial100.0 %
A277984a(n) = 6*n*(9*n-5)polynomial100.0 %
A277985a(n) = 3*(9*n - 1)*(3*n - 2)polynomial100.0 %
A277990a(n) = 54*n^2 + 6*npolynomial100.0 %
A277991a(n) = 81*n^2 - 9*npolynomial100.0 %
A279607Beatty sequence for e/2; i.e., a(n) = floor(n*e/2)Beatty11.2 %
A279895a(n) = n*(5*n + 11)/2polynomial100.0 %
A280089a(n) = 4*n^3 - 3*n + 1polynomial100.0 %
A280273Primes p such that 8p^2 - 7p + 2 is also primeprimes50.1 %
A280304a(n) = 3*n*(n^2 + 3*n + 4)polynomial100.0 %
A281093Primes having only {3, 4, 7, 9} as digitsprimes28.7 %
A281381a(n) = n*(n + 1)*(4*n + 5)/2polynomial100.0 %
A281437Primes of the form 25*n^2 + 25*n + 47primes100.0 %
A283394a(n) = 3*n*(3*n + 7)/2 + 4polynomial100.0 %
A284290Primes containing a digit 4primes25.6 %
A284291Primes containing a digit 6primes25.3 %
A284292Primes containing a digit 8primes25.4 %
A284293Numbers using only digits 1 and 6digit rule16.5 %
A284379Numbers k with digits 3 and 5 onlydigit rule15.7 %
A284380Numbers k with digits 5 and 7 onlydigit rule15.3 %
A284381Numbers k with digits 5 and 8 onlydigit rule14.2 %
A284632Numbers n with digits 2 and 6 onlydigit rule14.0 %
A284633Numbers n with digits 3 and 6 onlydigit rule11.1 %
A289134a(n) = 21*n^2 - 33*n + 13polynomial100.0 %
A289250Primes p such that p + 4 is a semiprimeprimes34.6 %
A289839Primes of the form 8*n^2+8*n+31primes100.0 %
A292509Primes of the form k^2 + 23*k + 23primes100.0 %
A292578Primes of the form 11*n^2 + 55*n + 43primes100.0 %
A296507Numbers m such that m^2 - 13 is a primeprime values18.5 %
A296716Numbers congruent to {7, 11, 13, 29} mod 30residue class18.6 %
A298360Numbers congruent to {3, 7, 13, 27} mod 30residue class30.9 %
A299250Numbers congruent to {9, 11, 21, 29} mod 30residue class33.9 %
A301451Numbers congruent to {1, 7} mod 9residue class22.5 %
A303740Primes of the form 9*k^2 + 3*k + 1primes100.0 %
A305859Numbers that are congruent to {1, 3, 11} mod 12residue class20.4 %
A307913Numbers without the decimal digits 3, 6 and 9digit rule11.5 %
A308269Primes p such that 2*p^2 + 2*p - 9 is primeprimes51.7 %
A309726Numbers k such that k^2 - 12 is primeprime values28.7 %
A317633Numbers congruent to {1, 7, 9} mod 10residue class13.8 %
A319279Numbers that are congruent to {0, 3, 7, 10} mod 12residue class11.3 %
A319280Numbers that are congruent to {0, 4, 7, 11} mod 12residue class15.0 %
A319452Numbers that are congruent to {0, 3, 6, 10} mod 12residue class11.7 %
A320752Primes of the form 5*n^2 - 5*n + 13primes100.0 %
A321212Numbers that are congruent to {2, 3} mod 16residue class20.3 %
A328058Primes p such that 2*p-1 is a semiprimeprimes35.4 %
A329106Primes containing at least one of the following digits: 4, 6, 8, or 9primes23.4 %
A329760Primes without {2, 7} as digitsprimes26.4 %
A332797Numbers whose smallest prime factor is 23multiplicative17.3 %
A332798Numbers whose smallest prime factor is 19multiplicative16.8 %
A332799Numbers whose smallest prime factor is 17multiplicative16.3 %
A334294Numbers k such that 70*k^2 + 70*k - 1 is primeprime values16.3 %
A338477Numbers k such that 398*k^2 - 1 is primeprime values16.6 %
A343810Numbers that contain only the digits 0,4,8digit rule10.8 %
A344872Semiprimes of the form 3m+2multiplicative27.5 %
A350676Primes p such that p^2 + 2*p + 4 is primeprimes50.3 %
A350856Initial members of prime triples (p, p+2, p+14)primes61.1 %
A352800Numbers k such that 2*k^2 + 29 is primeprime values16.9 %
A353004Numbers k such that 2*k^2 + 29 is semiprimemultiplicative13.2 %
A356498Primes p such that 100*p + 11 is also primeprimes46.0 %
A359555Primes p such that (p-2)^2 + 2 is also primeprimes48.3 %
A360652Primes of the form x^2 + 432*y^2quadratic form51.2 %
A360739Semiprimes of the form k^2 + 2multiplicative100.0 %
A360740Semiprimes of the form k^2 + 3multiplicative100.0 %
A360741Semiprimes of the form k^2 + 4multiplicative100.0 %
A361483Primes p such that p + 256 is also primeprimes47.3 %
A361484Primes p such that p + 512 is also primeprimes47.5 %
A361485Primes p such that p + 1024 is also primeprimes47.0 %
A361696Semiprimes of the form k^2 + 5multiplicative100.0 %
A361822Primes without {2, 5} as digitsprimes24.2 %
A365471Numbers whose digits are not all primesdigit rule9.6 %